Is there any limit to the quantity of AWS Lambda functions that can be executed at once?

No. The AWS Lambda is designed so that it can run some instances of functions simultaneously. However, AWS Lambda has a by default safety threshold for some consecutive runs for every account per region. The maximum successive executions for single AWS Lambda functions can be controlled which can be used to reserve a portion of the account concurrency threshold for the critical functions or lower traffic rates to downstream the resources.

If you so wish to submit a query to increase the limit, you can refer to the Support Centre for more.