At DFW all the terminals are connected by the SkyLink train. Even if you are not a fast walker, generally the max time between any gate is 15-20 minutes. So on arrival at DFW from SAN, no matter which terminal you arrive at, just use the nearest SkyLink train to head to terminal D which BA uses. No need to clear security on a domestic connection.

Arriving at DFW from LHR on the way to SAN, when you exit immigration/customs, you'll turn to the left where the bag drop will be on the right if you have checked bags, and then curve back around to the escalator up to security at D22. If the lines are long at that security checkpoint, keep curving back around to the left past the elevators for the Grand Hyatt, and there's another security checkpoint in the middle of the AA desks, that is typically faster than D22. Once you've cleared security at D, you'll know how long you'll have before your onward flight to SAN. The best lounges are in Term D as that is where most international flights depart. AMEX tends to be crowded, Flagship is good, and there's also a nice Capital One lounge. There are also Admiral's clubs in each terminal which you can access. So if you have a long time, you could always start with the Terminal D lounges, and then closer to flight time move to the AC closest to your gate.