You can't reach Lynchwood until after the mission "Where Angels Fear to Tread" but once you do, you'll find a large western city littered with bandits, bad sheriffs and showdowns.
Lynchwood has as many as six missions that start and finish within its bounds and a few more that start outside. You'll find yourself searching for legendary weapons in "the Bane", robbing a bank in "breaking the bank" and even having a showdown with a Sheriff of the town in "Showdown".