Heysham Port is associated with the Lancaster Group stations.
It is obviously valid via Carlisle/Lancaster, which is both the shortest and a mapped route. Mapped route additionally allows travel via the Cumbria Coast if you're that way inclined.
The other mapped route is TP+MH+NC. I've
queried this before for a Durham-Barrow-in-Furness journey. If the routeing guide is followed rigorously, it implies that YES it is valid via York and Leeds, but only if you travel in sequence on these maps.
This permits some odd routes but doesn't permit direct travel on the obvious routes between Leeds and Preston or Manchester and Preston (you must either travel Manchester-Bolton-Blackburn-Preston-Lancaster, or Leeds- Halifax - Blackburn - Hellifield - Wennington - Lancaster). You're in a situation where, if you want to travel on the York/Leeds-Preston train, your ticket is valid at all points along that route, but not for direct travel along that route. I suspect that this is an oversight and have used north-west to north-east tickets on Preston-York/Leeds services before with no problem.
EDIT
I should clarify that the maps mean that this ticket is also not valid for travel via Leeds-Skipton-Hellifield-Carnforth. Again, though, I wouldn't be surprised if your ticket was accepted on these services.