> Docker doesn't help distribute requests over IPs
That depends on your orchestration. AWS provide several tools for running Docker without having to maintain your own EC2 hosts.
> You can easily set up a launch configuration for EC2 that runs a script or program... But with a bit more work lambda will save a lot of money
You could do that via a launch configuration but that would be a pretty naff way of doing it. Baked AMI would be easier but personally I'd prefer ECS (Docker) or lambda. Cheaper, quicker to deploy, lower ramp up times.
Ultimately though, there's no wrong way to do this - just personal preference.
You can easily set up a launch configuration for EC2 that runs a script or program... But with a bit more work lambda will save a lot of money