I remain reluctant to answer when such requests for the
cheapest ticket are made, especially given that when the cheapest is offered, it's not uncommon that it turns out not to meet the passengers' needs.
Can you satisfy me that you've read my post #
11 from one of your previous threads please? (It may be worth having another read).
Again, I can only really repeat what has been said in your other two threads, that a London Midland Only ticket as far as London Midland will take you (in this case Crewe or Liverpool), and then another ticket from there, is quite possibly the cheapest.
It will be cheaper to take London Midland beyond Crewe, all the way to Liverpool (a Super Off Peak Return is £24.00), and then obtain another ticket from Liverpool to Lancaster (an Anytime Return LIV-LAN is a very reasonable £17.20). It's a lot slower than a fast, direct train. But it is highly likely to match the criteria of the cheapest, if that really is the only requirement!