I just checked my rule book to refresh my memory. Yes, the 35 Rem. is a legal cartridge for CLA.
The cartridge rule states: Any lever action center fire rifle 25 caliber or larger with a tubular magazine of original manufacture or replica thereof. A rimmed case loaded with a round or flat nosed bullet must be used. Exception:35 Remington is allowed.
In my wifes 35REM I load 19.0 Gr of IMR 4227 with a 158 REM FP out to Turkeys..... Lite recoil.... Ram load is 21Gr of IMR4227 with a REM 180 HP.... Moderate recoil and takes all but the very tuff Rams
I have shot a 336sc at the CLA matches at Wagner,SD since it is alegal caliber. Load is an RCBS cast bullet 200 gr FN. I'm running them at 1900 fps which is more velocity than needed but it is also a very succesful deer load.