I would like to know if there is a limit on the number of Lambda functions one can define (either per region or per account). To be clear I am not talking about a limit on the number of instances of a single lambda function, but instead on the number of function definitions that are allowed.
Looking at http://docs.aws.amazon.com/lambda/latest/dg/limits.html I did not find any explicit limit. There is a limit on the "Total size of all the deployment packages that can be uploaded per region" that is set to 75 GB, which indirectly limits the number of defined functions (for instance, if average size - across all of my lambda functions - of the deployment package is 40MB, then there is a limit of 75GB/40MB = 1875 functions per region).
As you found on the AWS Lambda Limits page, there is no current limit on the number of AWS Lambda functions per region or account.
You are correct, that there is a limit on Function and Layer Storage. That is described as "The amount of storage that's available for deployment packages and layer archives in the current Region." By default, this is set to 75 GB per region. However, this limit is adjustable. If you're getting close to this limit, you can request a quota increase and expand your indirect limit on the number of functions or layers.
Check out the Service Quotas service to see your current hard and soft limits for AWS services and request quota increases.
To request an increase in function storage:
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