Sync API on AWS GW, but ASYNC Lambdas?

Hi there,

Is it possible SOMEHOW to have an endpoint on the gateway that is SYNC to the caller (with a Timeout) and Async to the lambdas downstream?

For example, the FRONT END application calls my API (AWS), then a Lambda is invoked, checks and transforms the payload, in case it is OK the same lambda calls a remote service (outside AWS), this remote service might take 5 ~ 10 seconds… I would like to avoid leaving my lambda sitting there doing nothing (and being charged). What I would like to do is to call the remote service from my lambda and wait for a callback (webhook) which would be handled by an incoming Lambda… I would then identify the original request (TX_ID) and return to API GW, which would return the response to the correct caller (if no timeout was reached already).