LightDM is a cross-desktop display manager that was developed by Canonical. It was used as the default display manager in Ubuntu from 11.10 to 17.04 after which it was replaced with GDM. It continues to be part of Ubuntu and other distributions and is used by the smaller desktops as a display manager.
Since it was no longer the default display manager in Ubuntu development resources have reduced, but it continues to work. There is some bit rot that has occurred as things change around it.
All development is done in GitHub. You are welcome to file issues and pull requests there. Discussion is done here on discourse.ubuntu.com. Note that even though this is the Ubuntu discourse, LightDM is still expected to work on other distributions and this is not an indication that this project only relates to Ubuntu.
LightDM used to follow a release cycle that matches the Ubuntu release cycle. Currently no releases are being made, you can either use the most recent release or use the main git branch. The main branch should always be usable.