I lost my ID last summer on a trip to Denver.
Went to the checkpoint and stated I didn't have my ID. Someone came over and began asking me how I lost it (which was funny, if I knew how I lost it it wouldn't be lost would it?). She still wanted to see a picture ID, and eventually my Costco card did the trick.
Before heading down to security I checked with UA, and they said I might have to go through additional screening, but they let me through for regular screening.