Lentekhi is a small town high up in the Georgian Caucasus.
Walk out of the center and cross both bridges. You'll get to a roundabout and if you walk about 50 meters after the roundabout you'll find a good spot to start hitching.
It's basically one car every 5-10 minutes so you might have to wait a little bit. Most of the traffic goes in direction Kutaisı so if you wanna go to Ambrolauri you'll probably have to accept a ride to the intersection and find a new ride there.