In case someone is looking to move their java REST server to Lambda, here are a few lessons I learnt:
a) fragment your REST war into smaller micro services wars. The load time for big REST application will impact your caller. Small micro services will boot up on Lambda much faster and respond quicker.
b) If you use spring dependency injection, you may want to rethink that and tweak/optimize it. I had a database tier with over 20 hibernate/ebj beans . The load time was horrendous. I had to eliminate all beans not needed by the microservice.