AWS subnets for lambda synchronous invocations
I don't entirely understand your use-case, but it sounds like you are trying to limit the number of Lambda invocations by restricting its IP range.
There are two better ways to rate limit your application. Option one would be to use API Gateway request throttling:
https://docs.aws.amazon.com/apigateway/latest/developerguide/api-gateway-request-throttling.html
Option two, Lambdas have a concurrency limit that can be set to achieve a similar behaviour to your approach:
https://aws.amazon.com/about-aws/whats-new/2017/11/set-concurrency-limits-on-individual-aws-lambda-functions
Hope that helps with your design!