Best bet is to check out Cogganfield's pricing digest. He keeps track of sale activity of a lot of the older models. He has a sticky at the top of the page. What you are looking for is near the bottom of his lists. He also has a tip or two about rarity. I think you'd better buy it and post lots of pics.
The CLLM is very scarce, much, much scarcer than CLLE mk. I* or even the CLLE mk. I (the latter of which is itself very, very uncommon). Many CLLMs were upgraded to CLLE mk. I*.
Once in a while you see a commercial CLLM, known as the Territorial service pattern rifle. The actual military conversion types are hardly ever seen.
You do not state which the one you are interested in is, the military conversion type or the commercial Territorial type. Either way, it should be a keeper.
New Hampshire dealer Joe Salter sells the Territorial ones for $2,400-2,500 apiece on the rare occasions he has them (though these tend to be in near mint condition). I personally have never seen anyone sell a military conversion one.
This is what I think you should do: buy it without worrying too much about the price (within reason). There is little way for you to lose money, it seems to me. Then, when you are bored with it, sell it to me right quick!
Once you have bought it and posted pics, I would appreciate it if you’d be good enough to e-mail the price you paid, so that I can include it in next year’s price guide. Your name will not appear in the guide. You can reach me through the forum.