The National Trust list of properties doesn’t have much in this area. Rufford Hall and Formby are the two most local sites. Gawthorpe Hall is in East Lancashire. Then you head into Cheshire or Cumbria for the next ones.
Across England; Lincolnshire and Norfolk seem to be similarly poorly represented. Is it that these were more cut-off when large properties were being built, are they in private hands or council owned. Probably the first. In the area I can only think of Lytham Hall that might be of enough stature to become an NT property although it hasn’t much inside it.
At over £70 a year for a family membership you need to visit at least 6 properties a year to get value from your membership, although some might not view it that way. After a while Dunham Massey, Quarry Bank Mill and Tatton Park become a bit too familiar. Speke Hall is quite good but it’s a bit close to the city and not as relaxed to reach. The best houses in Cumbria are privately owned: Holker and Levens.
National Trust, what are you doing for Lancashire?