I've put Leica lenses on FSU bodies -- Went out and took pictures with them too.
Part of the great fun and attraction of LTM is the wide interchangeability of kit. I put Canon lenses on Leica bodies, Minolta on FSU, FSU on Canon, and the permutations go on.... I also like finding those oddball LTM items out there. Lenses from companies I never knew existed (or briefly mentioned on some obscure website). My "Arco" brand 135/3.5 LTM lens turned out to be sharp and accurate on many bodies. Minolta LTM lenses don't get much press, but my 45/2.8 is a good performer. And what's up with those "Sun" brand lenses? Ever see one of those in person? Zunow? (I wish)
Check out the LTM lens camerapedia page; quite a few lenses made to this "standard".
Now that non-FSU suggestions are gaining momentum, I support the Canon suggestions. Nice cameras all of them. Also, the Tower (Nicca) bodies are really quite nice, and some of them are the camera the Leica should have been.
And, in my opinion, actual Leica bodies a real value these days and can be quite inexpensive. You just need to be a little savvy to get a great Barnack (let's say a IIIc) for $200 -- and that could be a working camera that has possibly seen a CLA in its recent past, or at least its in good working order at time of purchase. I've seen just such a camera here on RFF classifieds recently. You can find Leica bodies for less than $200 with the understanding that they need service. A basic CLA service from Youxin Ye is quite reasonable. You will hear praise and criticism for this repair person, but I think for a basic Barnack CLA, his service would be good.
If it hasn't been mentioned before, I'll mention it now: The RFF Classifieds is a good place to find a camera offered by a knowledgeable seller, and known history, and fair price. I'm much more willing to believe "recent CLA" here than the giant auction site. That statement actually means something here. They haven't been too frequent lately, but Canon RF, Leica Barnack, Tower/Nicca, and even FSU can be found on RFF Classifieds. There's a cute little Minolta II LTM in there right now. Price is right and for a working Minolta, who else on the block has one of those? Right?