If the dub-LHR get cancelled then you could ask to start the journey in LHR especially if you find an understanding agent. However even if the DUB-LHR get cancelled the expectation is just to rebook you on a later flight on the same route. Or you could argue you would like to go from DUB-JFK straight as the arrival to New York would be very important for you for example. It’s all above just speculation of course and just give you some idea what you could do.