Being on a leash isn't necessarily bad, but I'd be concerned that a cat kept on a leash all the time would not be able to take care of its needs. Like any other animal, it needs to be able to eat, drink, exercise, and relieve itself freely. I'm especially concerned about drinking and relieving itself because cats can be prone to UTIs and kidney problems, which are made worse if the cat is not taking care of its basic needs as it should.
As for the question of staying on her lap most of the day, cats in the general spend a great portion of their day sleeping, and cats of certain temperaments will be content to even laze around all day. It's very unlikely that the cat could be made to do this if it weren't already inclined to. Cats would generally squirm and try to escape if they didn't. However, some attempt should be made to play with the cat even just a small amount every day, as all animals get many benefits from exercise. In the end though, this may not be very possible for some cats who are too much of a couch potato to get moving, and you can't exactly force a cat to do anything.
In conclusion, I think it's likely the cat is probably happy with this lifestyle as long as it can freely take care of its other needs, and as long as it's getting some decent exercise in the form of walks, it is probably okay.