Hi bezo, hi Isleofgough,thank you for the answers!
I'm running R18 (on Windows 10), used live selection all the time.
Since I'm the noobest noob I didn't know the shortcut, tried double clicking (also because of Houdini hehe) - and it worked just fine until yesterday evening.
I tried copying the mesh into the new file and back - it also doesn't work. What is really strange is that even if I create a new cylinder or any other mesh with loops in the first file - also can't use double clicking. And in the same time in a new file I can do it with all meshes - copied from the first file or just created, in the same mode with the same live selection tool. Feels almost like the file is corrupted in some odd way ><
But! Isleofgough's tipp about U>L keystrokes works for every file. So i guess I'll keep using it. It's still way faster and handier then going to loop cut button in the menu. Thank you very much for your help!