I am not sure if there even is a lounge in the international terminal. OVB has a business lounge and a VIP lounge (which likely incurs a fee), but to my knowledge they are both in the domestic terminal (possibly serving international passengers as well).

They'd likely require passing immigration (check visa requirements).

Onsite at OVB is a modern and comfortable hotel - http://www.skyport.su/ - just a 5 min walk from the terminals. I stayed there once, and liked it overall.