sit vs lie

Hi,
Surely not the $64,000 question, but still: how you choose between ‘lie’ and ‘sit’ when dealing with position of smth, eg “The house sits on top of a hill” \ in a particular place.
“London lies on the Thames.” \on a particular surface\
But: “The tins looked as though they had been sitting on the shelf for months.” “My climbing boots were sitting unused in a cupboard.” “He’s got a computer sitting on his desk, but he doesn’t use it.” – If “boots sitting unused in a cupboard” fits in the pattern ‘in a particular place’, what makes a computer or the tins sit rather than lie ‘on a particular surface’ (saving much more energy)?
And what about your hankie: is it sitting\lying in your pocket?
Thank you.

I think it depends on the dimensions, shape and usual orientation of the object. It doesn’t have anything to do with the difference between in a place or on a surface,
Tins ‘sit’ because they are not laying on their sides (rounded faces) in the cupboard. They are generally taller than they are wide. If they were on their side they could ‘lie’,
A computer ‘sits’ because it is upright on a stand. It is were on its back it would lie.
With boots, either can be used. You can think that they sit or lie on the soles. I’d see nothing wrong with boots or shoes that are said to lie in a cupboard.

If anything, I suppose a hankie could be described as sitting in your pocket.