FULL PRODUCT VERSION :
javac 1.8.0_91
java version "1.8.0_91"
Java(TM) SE Runtime Environment (build 1.8.0_91-b14)
Java HotSpot(TM) 64-Bit Server VM (build 25.91-b14, mixed mode)

ADDITIONAL OS VERSION INFORMATION :
Mac OS X Darwin Kernel Version 14.5.0: Thu Apr 21 20:40:54 PDT 2016; root:xnu-2782.50.3~1/RELEASE_X86_64 x86_64

A DESCRIPTION OF THE PROBLEM :
ClassCastException is thrown by Java8 upon deserializing a lambda when following conditions are met:
- Parent class has a method, reference to which is used to automatically create a Serializable lambda
- There are several child classes that extend it and there are several usages of above method as a method reference, but with different child classes
- After method reference is consumed it is serialized and the deserialized
- All method references are used within the same capturing class

Please see attached code and actual output for more details.

Also I have made some additional analysis. Upon decompiling this $deserializeLambda$ method with CFR following code is revealed:

private static /* synthetic */ Object $deserializeLambda$(SerializedLambda lambda) {
    switch (lambda.getImplMethodName()) {
        case "convert": {
            if (lambda.getImplMethodKind() == 5 && lambda.getFunctionalInterfaceClass().equals("LambdaSerializationTest$MyFunction") && lambda.getFunctionalInterfaceMethodName().equals("call") && lambda.getFunctionalInterfaceMethodSignature().equals("(Ljava/lang/Object;)Ljava/lang/Object;") && lambda.getImplClass().equals("LambdaSerializationTest$AbstractConverter") && lambda.getImplMethodSignature().equals("(Ljava/lang/String;)Ljava/lang/String;")) {
                return (MyFunction<String, String>)LambdaMetafactory.altMetafactory(null, null, null, (Ljava/lang/Object;)Ljava/lang/Object;, convert(java.lang.String ), (Ljava/lang/String;)Ljava/lang/String;)((ConverterA)((ConverterA)lambda.getCapturedArg(0)));
            }
            if (lambda.getImplMethodKind() == 5 && lambda.getFunctionalInterfaceClass().equals("LambdaSerializationTest$MyFunction") && lambda.getFunctionalInterfaceMethodName().equals("call") && lambda.getFunctionalInterfaceMethodSignature().equals("(Ljava/lang/Object;)Ljava/lang/Object;") && lambda.getImplClass().equals("LambdaSerializationTest$AbstractConverter") && lambda.getImplMethodSignature().equals("(Ljava/lang/String;)Ljava/lang/String;")) {
                return (MyFunction<String, String>)LambdaMetafactory.altMetafactory(null, null, null, (Ljava/lang/Object;)Ljava/lang/Object;, convert(java.lang.String ), (Ljava/lang/String;)Ljava/lang/String;)((ConverterB)((ConverterB)lambda.getCapturedArg(0)));
            }
            if (lambda.getImplMethodKind() != 5 || !lambda.getFunctionalInterfaceClass().equals("LambdaSerializationTest$MyFunction") || !lambda.getFunctionalInterfaceMethodName().equals("call") || !lambda.getFunctionalInterfaceMethodSignature().equals("(Ljava/lang/Object;)Ljava/lang/Object;") || !lambda.getImplClass().equals("LambdaSerializationTest$AbstractConverter") || !lambda.getImplMethodSignature().equals("(Ljava/lang/String;)Ljava/lang/String;")) break;
            return (MyFunction<String, String>)LambdaMetafactory.altMetafactory(null, null, null, (Ljava/lang/Object;)Ljava/lang/Object;, convert(java.lang.String ), (Ljava/lang/String;)Ljava/lang/String;)((ConverterC)((ConverterC)lambda.getCapturedArg(0)));
        }
    }
    throw new IllegalArgumentException("Invalid lambda deserialization");
}

We observe that LambdaSerializationTest$AbstractConverter is used as implClass instead of concrete LambdaSerializationTest$ConverterX. So all 3 lambdas will satisfy 1st if condition and ConverterA is always assumed.

STEPS TO FOLLOW TO REPRODUCE THE PROBLEM :
Please run the attached test case and observe the output.

EXPECTED VERSUS ACTUAL BEHAVIOR :
EXPECTED -
Output:
1.8.0_91
test_A
test_B
test_C
ACTUAL -
Output:
1.8.0_91
test_A
Exception in thread "main" java.lang.RuntimeException: java.io.IOException: unexpected exception type
    at LambdaSerializationTest.serializeDeserialize(LambdaSerializationTest.java:68)
    at LambdaSerializationTest.giveFunction(LambdaSerializationTest.java:52)
    at LambdaSerializationTest.main(LambdaSerializationTest.java:47)
    at sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)
    at sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)
    at sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)
    at java.lang.reflect.Method.invoke(Method.java:498)
    at com.intellij.rt.execution.application.AppMain.main(AppMain.java:144)
Caused by: java.io.IOException: unexpected exception type
    at java.io.ObjectStreamClass.throwMiscException(ObjectStreamClass.java:1582)
    at java.io.ObjectStreamClass.invokeReadResolve(ObjectStreamClass.java:1154)
    at java.io.ObjectInputStream.readOrdinaryObject(ObjectInputStream.java:1817)
    at java.io.ObjectInputStream.readObject0(ObjectInputStream.java:1353)
    at java.io.ObjectInputStream.readObject(ObjectInputStream.java:373)
    at LambdaSerializationTest.serializeDeserialize(LambdaSerializationTest.java:65)
    ... 7 more
Caused by: java.lang.reflect.InvocationTargetException
    at sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)
    at sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)
    at sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)
    at java.lang.reflect.Method.invoke(Method.java:498)
    at java.lang.invoke.SerializedLambda.readResolve(SerializedLambda.java:230)
    at sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)
    at sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)
    at sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)
    at java.lang.reflect.Method.invoke(Method.java:498)
    at java.io.ObjectStreamClass.invokeReadResolve(ObjectStreamClass.java:1148)
    ... 11 more
Caused by: java.lang.ClassCastException: LambdaSerializationTest$ConverterB cannot be cast to LambdaSerializationTest$ConverterA
    at LambdaSerializationTest.$deserializeLambda$(LambdaSerializationTest.java:7)
    ... 21 more

ERROR MESSAGES/STACK TRACES THAT OCCUR :
Exception in thread "main" java.lang.RuntimeException: java.io.IOException: unexpected exception type
    at LambdaSerializationTest.serializeDeserialize(LambdaSerializationTest.java:68)
    at LambdaSerializationTest.giveFunction(LambdaSerializationTest.java:52)
    at LambdaSerializationTest.main(LambdaSerializationTest.java:47)
    at sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)
    at sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)
    at sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)
    at java.lang.reflect.Method.invoke(Method.java:498)
    at com.intellij.rt.execution.application.AppMain.main(AppMain.java:144)
Caused by: java.io.IOException: unexpected exception type
    at java.io.ObjectStreamClass.throwMiscException(ObjectStreamClass.java:1582)
    at java.io.ObjectStreamClass.invokeReadResolve(ObjectStreamClass.java:1154)
    at java.io.ObjectInputStream.readOrdinaryObject(ObjectInputStream.java:1817)
    at java.io.ObjectInputStream.readObject0(ObjectInputStream.java:1353)
    at java.io.ObjectInputStream.readObject(ObjectInputStream.java:373)
    at LambdaSerializationTest.serializeDeserialize(LambdaSerializationTest.java:65)
    ... 7 more
Caused by: java.lang.reflect.InvocationTargetException
    at sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)
    at sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)
    at sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)
    at java.lang.reflect.Method.invoke(Method.java:498)
    at java.lang.invoke.SerializedLambda.readResolve(SerializedLambda.java:230)
    at sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)
    at sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)
    at sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)
    at java.lang.reflect.Method.invoke(Method.java:498)
    at java.io.ObjectStreamClass.invokeReadResolve(ObjectStreamClass.java:1148)
    ... 11 more
Caused by: java.lang.ClassCastException: LambdaSerializationTest$ConverterB cannot be cast to LambdaSerializationTest$ConverterA
    at LambdaSerializationTest.$deserializeLambda$(LambdaSerializationTest.java:7)
    ... 21 more

REPRODUCIBILITY :
This bug can be reproduced always.

---------- BEGIN SOURCE ----------
import java.io.*;

/**
 * @author Max Myslyvtsev
 * @since 7/6/16
 */
public class LambdaSerializationTest implements Serializable {

    static abstract class AbstractConverter implements Serializable {
        String convert(String input) {
            return doConvert(input);
        }

        abstract String doConvert(String input);
    }

    static class ConverterA extends AbstractConverter {
        @Override
        String doConvert(String input) {
            return input + "_A";
        }
    }

    static class ConverterB extends AbstractConverter {
        @Override
        String doConvert(String input) {
            return input + "_B";
        }
    }

    static class ConverterC extends AbstractConverter {
        @Override
        String doConvert(String input) {
            return input + "_C";
        }
    }

    interface MyFunction<T, R> extends Serializable {
        R call(T var);
    }

    public static void main(String[] args) throws Exception {
        System.out.println(System.getProperty("java.version"));
        ConverterA converterA = new ConverterA();
        ConverterB converterB = new ConverterB();
        ConverterC converterC = new ConverterC();
        giveFunction(converterA::convert);
        giveFunction(converterB::convert);
        giveFunction(converterC::convert);
    }

    private static void giveFunction(MyFunction<String, String> f) {
        f = serializeDeserialize(f);
        System.out.println(f.call("test"));
    }

    private static <T> T serializeDeserialize(T object) {
        try {
            ByteArrayOutputStream baos = new ByteArrayOutputStream();
            ObjectOutputStream oos = new ObjectOutputStream(baos);
            oos.writeObject(object);
            byte[] bytes = baos.toByteArray();
            ByteArrayInputStream bais = new ByteArrayInputStream(bytes);
            ObjectInputStream ois = new ObjectInputStream(bais);
            @SuppressWarnings("unchecked")
            T result = (T) ois.readObject();
            return result;
        } catch (Exception e) {
            throw new RuntimeException(e);
        }
    }

}
---------- END SOURCE ----------

CUSTOMER SUBMITTED WORKAROUND :
There are following workarounds available:
- Do not use such method references in same capturing class, but rather spread it by different (possibly inner) capturing classes.
- Do not use method references as actual arguments, but use inner classes instead.