Use MHs.lookup to look itself up. The resulting MH is broken. See attached test case, or the following snippet:

 Lookup lookup = lookup();
 lookup.findStatic(lookup.lookupClass(), "say", methodType(void.class, String.class)).invokeExact("hello, world");
 MethodHandle MH_lookup2 = lookup.findStatic(MethodHandles.class, "lookup", methodType(Lookup.class));
 // Next line gets IAE: illegal lookupClass: class java.lang.invoke.MethodHandleImpl$BindCaller$T/471910020
 Lookup lookup2 = (Lookup) MH_lookup2.invokeExact();

Suggested fix: Special-case the caller binding logic for lookup.

Consider doing this for any other hyper-sensitive @CallerSensitive method which looks at more than its caller class loader.