The Heysham ideas smell a lot of 'railway is the solution, what is the problem'.
The problem is surely that Lancaster is particularly badly congested, the buses (although frequent) are very slow, giving a big incentive to drive, and for all sorts of environmental reasons besides congestion, there's a need to get people driving less. For anyone wanting to travel further afield than Lancaster, public transport options from the whole urban area between Morecambe and Heysham are poor: You either have to bus into Lancaster then walk from Lancaster bus station to the rail station, or make your way to Morecambe and get the rather irregular train to Lancaster from there.
Also, Morecambe has for a long time been relatively deprived compared to Lancaster, largely because of the poor transport options - particularly for getting to the University. That also has knock-on effects in Lancaster, making housing and renting pretty expensive there because, basically 10K+ students are trying to cram into Lancaster with relatively few willing to live in Morecambe because that makes commuting to the University so long/difficult. That sounds at first sight not relevant to Heysham - except that if the railway can pick up passengers from Heysham, that helps to give you a critical mass of passengers that makes it sustainable to run a much better service from Morecambe too.
Also, worth pointing out that, although in this thread we've been discussing very expensive infrastructure to provide Morecambe with a more frequent, clockface, service, providing some kind of service to Heysham doesn't require much infrastructure at all: All you basically need are a couple of basic one-platform stations (say as a minimum, one in Westgate, one a bit further South) where all you need to build are one platform, a couple of ticket machines, and a path from the road to the platform.