I think it's one of the best ideas ever posted here for a new station! Deserves a thread of its own. [Certainly more than than the mindless meanderings about reopenings in west Wales and SW Scotland <I dare not even breathe their names in here>.

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Ok, in truth, I don't know how big/important Lancaster University is in terms of daily journeys, but it also has a conference centre, so presumably there woulld be more than just students, profs and acnillary staff doing daily commutes. Maybe it would also serve as a P&R for south Lancaster?
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Gosh, I wasn't expecting that kind of positive reaction. Thanks!
The University is potentially huge as a source of commuting. According to
this page, 12K students, and I would guess at least a thousand staff. I'm guessing maybe half the students would live on campus, with most of the remainder living in Lancaster itself. And there's the hotel and conferences etc. Many years ago, substantial numbers of students also lived in Morecambe, but that tended to disappear during the 2000s - mainly I think because Morecambe to the Uni is such a slow journey by bus or car, and more student accommodation became available in Lancaster.
The students in Lancaster tend to live either in or south of the city centre (notably around Bowerham), since traffic in Lancaster is extremely congested, so almost anywhere north of the city centre will tend to give quite unpleasant and long journeys to the university. For most of those people, as well as those living in the Uni halls who want to get to Lancaster, the bus would still be most convenient, as it's extremely frequent (every 5-10 mins) and virtually door-to-door for many. A University station would be about 5-10 minutes walk from the centre of the University. Nearer 15 minutes for the departments and halls at the Southern end.
What I think a train would do is make it much more convenient for students and staff to commute from Morecambe (or from Preston), so you'd very quickly see substantial numbers starting to live there and using the train for their commutes. The same would happen to some extent in Marsh - a large housing area just west of Lancaster station, which currently has very poor road transport links (basically you can't get to anywhere without negotiating the traffic jams in Lancaster city centre first). and is therefore not convenient to get to the University from. A new station would also be used quite a bit by people coming from further afield - if catching a train at the University station could quickly get you to connections at Lancaster or Preston.
The nice thing about a new University station is that there is ample land round there to build it on, and you could basically site it virtually at the University main gates, where it would connect nicely with the local buses. Having ample demand for the station, land easily available to build it on, and frequent bus routes passing right next to the site is a rather nice combination that I suspect you wouldn't find in many other places in the UK.
The big problem right now however is of course that, even if you built a station at the University, there's almost nothing in the way of trains that currently run up that line that you could plausibly stop there - almost all trains are long-distance ones up to Scotland. That's where extending the Morecambe service so it runs Morecambe-Preston, or (better) Morecambe-Manchester, would come in, since that provides the trains that would stop at the University and also links the (hypothetical) station to all the housing in Morecambe too. Since Morecambe has for a long time been a relatively poor part of the area, I imagine, the impact on jobs etc. in Morecambe would be welcomed.
A new station would be what, 2 miles south of Castle station? It would then be a 10 min walk to the centre of the campus area? I confess, I'm not sure how well sited Lancaster Castle is for the city centre - last time I was on the platform there was a Standard 5 as station pilot
New station would be about 3 miles south of castle station. Castle station is about 5-10 minutes walk from the town centre, depending which bit of the town you want.