LHO was apparently changing his appearance after each time being sighted. T-shirt in the sniper’s nest, brown shirt in the lunchroom, T-shirt in Mrs. Reid’s office area, brown shirt in the bus/cab, changed into a light colored jacket, etc in the rooming house room, ditched the jacket after leaving the Tippit murder scene. LHO was apparently trying to make it more difficult for anyone to track him (much like “The Fugitive” does in that TV show). Having the cab drop him off a bit past the rooming house was another similar tactic for trying to make it more difficult for anyone to track him.
BTW, I am guessing he tried to get rid of some evidence when he spent the actual Carcano dime on the Coke…. 
He wasn't pretending to be anyone other than Lee Harvey Oswald, so "changing his appearance" between the lunchroom encounter and the encounter with Mrs. Reid, and then changing again before entering the bus, seems far-fetched. It's not clear to me what he would have gained by those gyrations. I can definitely understand changes at the rooming house - in fact, much bigger changes than he actually made (fake beard? Dallas Cowboys jacket?) if he'd really been planning ahead. My scenario has him in his white V-neck t-shirt during the shooting, slipping into his brown overshirt as he left the sixth floor, and Mrs. Reid simply not being a reliable witness. I don't know how many times I've spent all morning with my wife and then ended up looking for her in some store while thinking "What the hell was she wearing?"
