With LFS handling assets with Git shouldn't be a problem. From the sounds of it, the biggest problem they had here was not in the technology but GitLabs pricing which doesn't separate LFS storage. For example GitHub and BitBucket have separate pricing for LFS, both at more reasonable $.1/GB, i.e. five times cheaper than GitLab. If I'm reading it right Azure even offers LFS for free(!).
Technically I believe you can even have LFS hosted in different place than the repo itself, although I don't know if these commercial providers handle such case. But in theory you could host your git repo at gitlab.com and selfhost lfs if you want to penny pinch.
The one standout quality that git LFS has in my experience is the rate at which working copies with LFS enabled shred themselves and become unrecoverable. I've seen this on multiple projects and different users now and it doesn't give me the confidence I'd need to rely on it for a big project.
I'm sure that there will be people replying that this is anecdotal etc. But this is my personal experience and what shapes my recommendations.
I've been using it for many years now for data repos like photos. IIUC one advantage it has over LFS is its model makes it easier to store data in many different places (though I don't use LFS myself).
Technically I believe you can even have LFS hosted in different place than the repo itself, although I don't know if these commercial providers handle such case. But in theory you could host your git repo at gitlab.com and selfhost lfs if you want to penny pinch.