In case anyone runs into the same issue, here's how to fix it:
Stop the Gitea container and change into the following folder:
appdata/gitea/data/gitea/conf
Edit the app.ini file to the following:
Comment out this line:
[server]
...
#LFS_CONTENT_PATH=/data/git/lfs
Add those lines:
[lfs]
PATH=/data/git/lfs
Start the Gitea container.