No, he (allegedly) said that he brought his lunch to work, not that he carried a bag inside the TSBD.
Agreed. Dougherty didn't just say he didn't notice anything. He said Oswald was empty-handed.
Question:..... How reliable was Dougherty? I think he was peeing down his leg when he was being questioned....
The dim bulb could have easily overlooked a normal lunch sack....But I doubt that he would not have noticed that Lee was carrying a giant bag if Lee had been carrying such a large and unusual bag. ( which raises another point..... Apparently most of the other workers were right there on the first floor getting ready to start their day, when lee entered the building. If he'd have been carrying an unusual size sack surely someone would have noticed...