In this instance you wouldn't need to worry because you'll check all your luggage in IAH (with your business allowance) and that will be through-checked to EDI (unless you have a stopover at LHR). Also you would get 2x 32kg bags on a business class booking.

A very very general rule is that the longest leg determines your baggage allowance. So even if your EDI-LHR was in Y, you would get J baggage allowance as you connect straight onto LHR-IAH.