Consider the following example

class Test {
    @Target(ElementType.TYPE_USE)
    @interface TypeAnno { }

    @TypeAnno Supplier<String> r_f_i = () -> "r_f_i"; // ok
    static @TypeAnno Supplier<String> r_f_s = () -> "r_f_s"; // ok

    {
        @TypeAnno Supplier<String> r_init_i = () -> "r_init_i"; // missing
    }

    static {
        @TypeAnno Supplier<String> r_init_s = () -> "r_init_s"; // missing
    }

    void m() {
        @TypeAnno Supplier<String> r_m_i = () -> "r_m_i"; // missing
    }

    static void g() {
        @TypeAnno Supplier<String> r_g_s = () -> "r_g_s"; // missing
    }

    void h() {
        t_cr(() -> "t_cr"); // ok
    }

    void i() {
        t_no_cr((@TypeAnno Supplier<String>)() -> "t_no_cr"); // ok
    }

    void j() {
        t_no_cr((java.io.Serializable & @TypeAnno Supplier<String>)() -> "t_no_cr"); // ok
    }

    void t_cr(@TypeAnno Supplier<String> r_p) { }
    void t_no_cr(@TypeAnno Supplier<String> r_p) { }
}

This demonstrates the use of type annotations on variable declarations with a lambda initializer. By manually inspecting the AST, it's possible to see that the type annotations are missing in the lambda target type in the cases highlighted (local variable declaration).