Won’t a fair proportion of the traffic come from people already holidaying in the area, such as at Blackpool or the lakes? These people aren’t going to be an easy target for train travel.
Yes, but part of the planning/proposal is pedestrianisation of quite a large part of the promenade around Eden site, removal of the car park on the site, and a clear expectation that visitors will get there by means other than driving. There are no new car parks proposed, and the whole project is based on the environment. The question is how visitors will get there if not by car.
There's a discussion about a new bus service from the Lancaster park n ride site, but it's car park isn't particular large and it's quite a long/boring bus journey that will feed into the already busy/congested Morecambe Road/Shrimp Roundabout/Lancaster Road corridor. Seeing as the train station is within easy walking distance, it would make sense to use the line/station to get at least a fair proportion of visitors there, but significant changes are needed, least of all some kind of park n ride system using the trains.
It's a shame that there is no obvious way of using the Hest Bank line so shuttle trains to Morecambe can at least avoid Carlisle Bridge and Lancaster station, i.e. either an expanded car park for PNR at Carnforth, or a new "halt" on the barely used 3rd track at Hest Bank (using the shore as the car park and reinstating a platform at the site of the old Hest Bank station on the spur line only), both options have pretty big drawbacks, mainly car park sites being too small.
I do think there are two aspects here. One being for travellers to come the full journey by train, i.e. from Manchester, Liverpool, etc., and the other for a more local/short service from a park and ride car park to "catch" the travellers coming by car. Two different solutions needed for two different target markets.