Really you only have 45 minutes because of the check in / bag drop close time. Well even less than that because you don't want to present yourself dead on 45 minutes and finding a queue!

last time I was at DUB the bags took an age to arrive for some reason - at least 10 mins if not more of waiting at the belt after clearing passport control where I was first in the empty queue. Though this was for an early evening arrival ex LCY on BA so a mid day arrival could be very different. (Note I wasn’t doing a B2B but staying over)

How long do you have between your arrival at LHR and your departure to JFK because an option might be to use the airportr service which would cut that hassle for you at DUB but you’d need time to retrieve the bags from them and check them in at T5 when you arrived there. They may not offer the check in service for pax checking in bags mid way through a trip though it could be worth looking at. They do offer a LGW - LHR delivery service though their delivery times may mean you have to get to LGW earlier to meet those.

is there no way you can position from LHR?