I have three lavateras in my garden cos we like em. One i am concerned about see "More details" of my query.

Depends how close it is to the swimming pool - lavateras should be cut down in late March/early April (depending on where you live) anyway, a bit like Buddleia, where you chop it down and let it regrow (to about 10 feet usually) for flowering. This restricts their root spread to some extent because you're restricting the overall size of the plant. It is not, though, a tree and I wouldn't anticipate its roots spreading much further than six feet out from the main stem at the most. How far down they go I'm not sure. They're also not long lived and may just suddenly die.

I dug up a large lavatera 2 years ago because it had died and although the branches at ground level were thick like yours the roots were not too enormous. Definitely the roots of a shrub rather than the very strong roots of a tree. I think the thickest roots spread about a metre but then became less . I would be surprised if they would damage the thick wall of a swimming pool.