While Western-style 'thrones' are now found in most midrange and top-end accommodation, budget travellers should expect the rather-less-royal squat toilet to be the norm when staying in some guesthouses and particularly homestays.
Even in places where sit-down toilets are installed, the plumbing may not be designed to take toilet paper. In such cases there will usually be a rubbish bin for used paper.
Public toilets are uncommon outside hotel lobbies and airports. While on the road between towns and villages it's perfectly acceptable to go behind a tree or use the roadside. Lao tour guides use the euphemism 'shooting rabbits' for men and 'picking flowers' for women in case you wonder what on earth they are talking about.