Although the details of the OP's trip pose a couple of practical issues.

The DUB-LHR returns to T5, but the next day's LHR-DFW departs from T3. So there is an inconvenience whether it's dropped at T5 left luggage or T3 left luggage that evening.

In addition, the OP is not returning from DUB to LHR on the same aircraft as the LHR-DUB, which could make things tricky if the LHR-DUB aircraft is running late but the DUB-LHR aircraft is not. A couple of months ago, some FTers were doing LHR-DUB to start ex-DUB tickets, but that precise situation developed - illustrating the repeated advice that there is probably more risk to flying LHR-DUB on one rotation and returning DUB-LHR on the next, than there is flying LHR-DUB-LHR on the same aircraft. However, as the OP here has a checked bag, the same aircraft turnaround thing won't work.

There's obviously still a risk in relying on QF short-checking the bag to LHR. But so long as QF does this, then my gut instinct is that the rest of the risk can probably be lived with. Even if the OP were to miss BA834 LHR-DUB, he would probably still be in time for BA836 LHR-DUB which is the outbound flight for BA837 DUB-LHR.