Back-to-back on the INBOUND:

I have a back to back booked on the way back of a viking booking JFK-LHR-OSL-LHR and I was wondering the following:

If my flight from JFK arrive to late and I can't take the LHR-OSL flight I was supposed to take, what would happen? Can I asked to be rebooked for the OSL-LHR leg or will BA encourage me to drop the last leg and stay in LHR? I really need to be back in LHR the following morning cause I have an AA flight to DFW to take.