From the research I did, here's how languages stack up in Lambda runtime (lowest first):
1. Python & JS
2. Go
3. C# & Java
I couldn't find any data on Rust.
The understanding at the time was that Python & JS runtimes are built-in, so the interpreter is "already running" Go is the fastest of compiled languages, but just can't beat the built-in runtimes. C# and Java were poorest as they're spinning up a larger runtime that's more optimized for long-running throughput.
https://docs.aws.amazon.com/lambda/latest/dg/best-practices....
https://medium.com/the-theam-journey/benchmarking-aws-lambda...
https://epsagon.com/development/aws-lambda-programming-langu...
https://read.acloud.guru/comparing-aws-lambda-performance-of...
Of course, benchmarks like this only go so far. Use as a starting point for your own evaluation; not as an end-all-be-all.