Well, your salary is something of a sunk cost. Now depending on the amount of time spent managing that GitLab server, it might make financial sense. If it is truly easy to maintain as they seek, and claim, then it just might make sense.
Consider the organization that needs hosted GitHub enterprise - a pricey proposition. Unless you could otherwise have spent your time working on a feature that would directly increase sales (which is probably unlikely in an enterprise locale) then your time really is just sunk cost.
So to recap, for the one-off private repo - probably easier and more sensible in terms of resources to use GitHub. For a large organization that has man hours to burn or otherwise needs an in-house hosted solution, GitLab (or Gogs) could make sense.
GitLab has been ridiculously easy to manage for us. Really my only complaint is that it's slow as all hell, and gives up too early on a lot of pages because of this.
Still, compared to the Perforce server crashing every other week (a slight exaggeration, but still), it's a marked improvement.
Consider the organization that needs hosted GitHub enterprise - a pricey proposition. Unless you could otherwise have spent your time working on a feature that would directly increase sales (which is probably unlikely in an enterprise locale) then your time really is just sunk cost.
So to recap, for the one-off private repo - probably easier and more sensible in terms of resources to use GitHub. For a large organization that has man hours to burn or otherwise needs an in-house hosted solution, GitLab (or Gogs) could make sense.