You definitely can get an Alexa skill off the ground without using Lambda, but there are a lot of little details with their authentication to work out. I'd highly recommend one of the libraries that are out there:
Go - https://github.com/mikeflynn/go-alexa/tree/master/skillserve... (full disclosure: I created this one)
Offical Java SDK - https://developer.amazon.com/public/solutions/alexa/alexa-sk...
Node - https://www.npmjs.com/package/alexa-app
...to name a few.