For better or for worse (actually, it’s totally for the better, but that may not be obvious), the menu is not necessarily a simple list you can edit. Most desktop environments (LXQt/LXDE included) follow a set of specifications published by Freedesktop. There are three files related to menus, two of which are really only relevant for submenus. Basically, you need to make sure that there’s a Desktop Entry in (generally) /usr/share/applications.
It’s fairly trivial to create a Desktop Entry but there is none in the git-gui package. It seems there’s a long standing bug report in Launchpad to fix this. This was pushed upstream to Debian (the bug report of which includes several independent solutions), where they supposedly pushed it upstream. Unfortunately, it’s linked to Gmane which went down and never came back up so I can’t exactly reference that. However, trawling the git mailing list, I do find a response to the author of the Debian bug report that seems positive. However, I don’t find anything in the upstream code and I searched for “Desktop Entry” which is a required part of the file.
If you ever wanted to be a committer to a major piece of open source software, not to mention one developed by the creator of the Linux kernel, here’s your chance. You even have the solution!