You can allow for recursiveness, while this is dangerous and requires failover mechanisms, can be done.

aws lambda put-function-recursion-config --function-name yourFunctionName --recursive-loop Allow

As per other solutions, using a FIFO queue will increase the complexity with no real benefits, since AWS recursiveness protection also detects when it happens in said scenario:

https://docs.aws.amazon.com/lambda/latest/dg/invocation-recursion.html