On a Sunday, the first train from Lancaster to Manchester departs at 11:24 (this is the Furness line). On Saturdays this is at 6:24. To Birmingham, the first train on Saturdays is 6:58, on Sundays 11:58. To Glasgow, Saturdays 6:64, Sundays 11:54. The pattern is true elsewhere as well: from Blackpool, first Saturday train departs 5:18, first Sunday train 11:21. Boston, Saturdays 6:13, Sundays 12:13. Lincoln, Saturdays 5:26, Sundays 11:05. It's not true everywhere, but it is in many places. For the rest of the day, the Sunday frequency is not much less than the Saturday frequency.
I've taken the first Sunday train from Lancaster to Manchester twice. Both times, the train was extremely busy. On neither occasion could I find a place to sit. On one occasion, people were left behind on the platform as they could not board the overfull train. Although a sample size of two is small, I will assume this train is always busy.
Considering that demand clearly outstrips supply on Sunday morning, why do trains start running so late?