Hahahahah... The 100 Years War is like a 1000 Years war
Well, I would like to have LK for Linux too, but the way I found until now is to use a particular Linux distro (Slax 6.1.2 from Slax.org in a 8GB flash drive), adding Wine (I don't remember now the version, but I put that in Superuser.com forum - if you want to see that now, pls search on that) and them launching the .EXE files inside apps/name_of_app/app. I did not tested with a lot of them, but I know that SysInternals apps called Process Explorer and Autoruns function (and I love to see it running each time I use my Slax flash drive).
I tested with some *LKL.exe files, but they does not launch anything. I think is is very easy to LK team to solve that, at least creating a LK menu for Linux and to put an additional file together with each app package to do the same task that *LKL.exe file, or to redesign the way LK menu and *LKL.exe files function to allow them to be functional using Wine.