What is the largest java application that can be run on aws lambda?

Context: I have a huge java monolith application running on EC2 servers, and there is a use-case where there can be a burst in requests to the app once in a while - and when there is, the EC2 servers cannot handle the load and I cannot scale by just throwing more servers there. Its a typical problem that can be solved with lambdas. How should I go about this transition?