The main question here is your request rate.

• If it's usually very high, then in most cases you shouldn't run into cold starts - and for the rare gaps, you can send a steady stream of "blank" requests that will keep the lambda's alive.
• You can also consider pushing all your incoming requests to an SQS, and then triggering lambdas based on the sqs capacity - this way you'll be able to provide a constant level of service even with the cold starts