There are a lot of different options if you would like to use Clojure with AWS Lambda. It all depends on what you want.
For a fast startup, you can use babashka or GraalVM native-image. Both will require custom runtime, but the latter will be slightly faster. On the other hand, native-image requires some experience with GraalVM and it’s a challenge to write a code that is easily compiled to an executable.
I’m biased since it’s my project, but I would highly recommend trying holy-lambda out. Some comparison of runtimes is here if you’re interested 
: holy-lambda/1-01-whatits.md at master · FieryCod/holy-lambda · GitHub.