I would recommend you install TeXLive directly rather than using the packages that come with Ubuntu (which are 2 years out of date and have bugs in them).
My wife uses Kile for editing, but Texmaker looks nice, too... especially if you don't want all the KDE libraries.
Kile doesn't seem to have any licensing information beyond GPL/BSD. You don't mention platforms but it's part of KDE, which is great for Linux but will also run on Windows and OS X (or anything UNIX).
What platform are you on? Since I'm a crazy software engineer, I use a LaTeX plugin in Eclipse, but that's probably not for you. I know a lot of Windows users like Led. Kile is wonderful, but I'm going to take a wild guess and say you're probably not a KDE user, so it would pull in a whole lot of extra stuff and probably not be worth it.
There are actually a couple wysiwyg front-ends for latex. That way you could get the convenience of a nice gui with the full capability of latex. The only editor I've used with some of these features is Kile, but I know there are others out there.
Don't have crouton installed on my Plus so can't test for ya, but Ubuntu does have an up to date arm build of lyx so I see no reason it shouldn't work. https://launchpad.net/ubuntu/+source/lyx/2.2.3-1/+build/12611155
Kile would be another option http://kile.sourceforge.net/
Kile isn't too bad. I used to use it when i was starting out and it is supported on Mac/Win/*Nix machines.
Now i just write my docs in vim
Edit: including link to Kile