Originally Posted by Scaeva
The photo can be picked up torn long before Lee knows he needs it to convince Doug to go outside however, so in many cases I don't think his motivation had anything to do with Doug.
In fact since most people go into the backroom before stepping outside with Doug, its a safe bet that most peoples' Lee picked up the photo before Lee knew that his brother was a walker, and was trapped outside with the key.
Lee's line right after he picks it up to Carley is "It's a photo of the family that owned the place. It might help us track down the keys"