According to Interceptor 1.1 specification, p.11
If an interceptor class that is only used as a method level interceptor defines lifecycle callback interceptor methods, those lifecycle callback interceptor method are not invoked.
This specification is talking about
one interceptor class having
two different types of interceptor methods (around-invoke and lifecycle interceptors).
I came up with an example of an interceptor class:
The @PostConstruct method of MyInterceptor won't be invoked as MyInterceptor is used as a method level interceptor.
However, in my previous example, there are two different interceptors, MyLifeCycleInterceptor and AroundInvokeInterceptor. The specification does not say the case when two different types of interceptors trying to intercept a method.