GitLab is, among other things, a source control (Git) host (for software code) and an issue tracker. Issues are pretty useful for keeping track of small-ish 'projects' (i.e. collection of related tasks) like fixing a bug in a program or adding a new feature to a program. They're also pretty useful for anything for which you'd want to use a checklist.
Checklists can be added to a comment on the issue or to the issue's description. You'll probably want to do the latter in almost all cases.
To be able to re-use a checklist, you should create an issue description template. Then, when you want to create a new 'instance' of the checklist, you'll create a new issue and pick the description template with the relevant or desired checklist. You can then mark individual items in the checklist completed as well a 'close' (i.e. 'mark completed') the entire issue itself.
You should be able to use the gitlab.com website on an iPhone and there may also be a native third-party iOS app that supports description templates; see this page for possibilities:
The biggest drawbacks to using GitLab are probably all related to it being aimed at people that work with or on computer software. GitLab is based on Git source control software that's considered somewhat hard to use, even for software professionals. You can almost certainly get away with not using Git directly – you should be able to edit the necessary files directly from the GitLab website. But the need to edit files, and the probably confusion surrounding how to do that for people that aren't software professionals, may be a significant barrier to this as a general solution for most people.