Let's assume that Mrs Robert's was correct when she said that she saw Lee leaving the rooming house and he was donning a jacket as he left.
The next time that we see Lee Oswald ( positive ID) is when he is dragged from the theater....He has no jacket. But isn't it logical that he would remove his Jacket in the theater? It was reported that he moved from seat to seat prior to the start of the movie.... Could he simply have left his jacket in the seat next to his when he changed seats and forgot to take it with him when he changed seats?
Mr. BREWER - And had brown hair. He had a brown sports shirt on. His shirt tail was out.
Mr. BELIN - Any jacket?
Mr. BREWER - No. (...)
Mr. BELIN - Any other clothing that you noticed?
Mr. BREWER - He had a T-shirt underneath his shirt.
Mr. BELIN - Was his shirt buttoned up all the way?
Mr. BREWER - A couple of buttons were unbuttoned at the time.