Talk to Dutch back in the camp to start this mission. This is more like an interactive cutscene so no combat is involved. Ride with Lenny back to the saloon in Valentine to have a good time. Interact with the bartender to start the cutscene.
A few drinks later, you’ll be under heavy influence of alcohol but you’ll still have to search for Lenny inside the saloon. Go upstairs to find him and to trigger more cutscenes.
After pissing outside, head inside the Saloon and look for Lenny once again. All of the people inside will look like him so you’ll have to talk to them to reveal their real identity. Just ask around until the real Lenny approaches you. After the cutscenes, you’ll wake up inside a jail cell. After paying the fine, you’re free to leave. Mission complete.