Installers on Linux are one of the hairiest issues.
Here's the thing: every Linux distro has its own packagers, its own versions of common libraries and often its own C++ compiler. What that means is that unlike on windows, you can't just make an executable and give it to Linux users and they'll run it.
Instead, the exe has to be compiled specifically for that distro. An Ubuntu version of a game won't work on the Slackware distro, which won't work on the Fedora distro, etc.
The workaround is to use the raw source-code and compile it yourself. You can imagine how tricky that often is - for some projects it's as simple as unzipping the source and running two console commands. For others, it's incredibly complex. Spring is in the latter category.
Remember that, in Linux, bundling in your dependancies into your program is *extremely* frowned upon. Each library is expected to exist once and only once on the client system - so while every SDL-based app on Windows will have their own copy of SDL, corresponding Linux apps are all expected to share SDL - if two versions of the same lib can't live side-by-side for some reason, and you need both versions, you're in trouble.
Because of this mess, the most common way to get packages for a distro is to get them from first-party sources. Most people getting programs for Ubuntu (the most popular Linux distro) don't download them from other companies... they use the integrated package-fetching system (apt) and it pulls down the program and all its dependancies from Ubuntu's main servers. It's too much truoble to get X working right, so we just trust Ubuntu to do it for us - we open up the package manager and say "I want XXX" and it fetches it for us and configures it for our system seamlessly and silently, and has a built-in updater.
Kernel Panic, for example, is already in Ubuntu's repository. However, the version that lives in the repo is limited by the 6-month release cycle. It may not even be able to go online since it's running an old version of the Spring engine itself.
Ubuntu only allows their packaging system to be updated once every 6 months. So if you want to release anything that isn't a pure bugfix for a dangerous problem between now and the next release? Too bad.
So, because of that, we have PPAs. PPAs are plug-ins for the packaging system where the user can say "I want to add this repository so I'm not just getting stuff from Ubuntu, but this Ubuntu-compatible thing that's updated more than twice a year". Spring has its own PPA for this here:
https://launchpad.net/~spring/+archive/ppa
You can also create .deb and .rpm installers, which are analogous to installers under Windows, but they generally aren't popular these days.
Probably the best approach would be to see if you could get all Gundam's content packed up into a release on the Spring PPA and add SpringLobby as a dependancy. Then you'd have to give players instructions how to add the Spring PPA and then tell them to fetch Gundam - fetching Gundam would in turn fetch the lobby, which would in turn fetch the engine.
This will get you into Ubuntu which is the most popular Linux version. Debian is often compatible with Ubuntu, but no guarantees, and there are several unofficial Ubuntu derivatives that are generally compatible with mainline Ubuntu - EG Mint.
Really, installing software is something that seems shockingly simple that, unless you're willing to play nice with the 1st-party sources, is actually really pathetically overcomplicated.