Serverless runtimes don't shut down the instance immediately after the invocation is complete but keep it up for an undetermined time depending on many factors (usually ~15 minutes) in order to process a possible new event without the start-up overhead (cold start). This means that in a system with constant traffic some instances may have a surprisingly long uptime. The instance gets destroyed when it throws an error though so a function with a disabled GC would clean the state when it runs out of memory. Slower processing done by memory-starved instances would probably eliminate any minimal performance gain you could get by disabling the GC though. (EDIT: I just realized that with no GC desperately spinning in place the starvation would not have much performance impact so this would actually be a very interesting approach if you can tolerate some invocations erroring out on out of memory errors, sorry!)
In regards to performance optimization of Lambdas, start-up time is the most important factor as cold starts happen also in cases of concurrent requests when no warm instances are available. This means that Go, Node and Python are pretty sweet for serverless. Thanks to recently released Lambda SnapStart feature that launches new instances from snapshots taken after application initialization Java (even with DI frameworks) is a plausible option if you're inclined that way. Previously you had to use a custom runtime and AOT compilation (that rules out any runtime DI stuff) to achieve tolerable performance with Java on Lambda.