As luck would have it someone made a dockerized version (sameersbn on github) of it. We've been using it at work for the past couple months without any hiccups.

It took a bit in the beginning because of a bug in one of the docker backends that was on by default, but following the guide he provided was simple. We opted to use the built-in redis and sql servers.

Link: https://github.com/sameersbn/docker-gitlab