In reply to OneBeardedWalker:
Ak Sai travel is the largest adventure travel and mountaineering company in Kyrgyzstan, they run the basecamps for all the major summits, and would be a very reliable company to go through if you want to climb Peak Lenin (most western agencies will work through them if you want to cut out the middle man).
They can also arrange Helicopter transfers, other transport and expedition supplies if you want to go to more remote locations.
https://ak-sai.com/en/
Also, don't overlook Ala Archa as a place to climb (next to Bishkek), it probably has some of the best quality mountaineering in the country.
Cheers,
Alex.