Used to be a hard quota of 29 seconds for APIGW, but within the last month AWS has updated that to a soft quota. You will have to trade off concurrent calls for the longer APIGW timeout though.
Use ALB - no limitations on request time.
Well, the point is you want a short timeout if your lambda is hanging and you're being billed by the second. If you're not setting it explicitly when you deploy, you're more or less writing Amazon a blank check.