The basic requirements for paper for lithography are flatness, good dimensional stability, neutral pH, ink receptivity and resistance to picking. The goal is to use a paper that makes good contact with the ink on a plate. This is a factor of the pressure used as well as the texture and softness of the paper.
Better papers can be printed dry or wet, each with its advantage. Dry paper won't stretch nearly as much as dampened paper but requires a lot more pressure to push the paper onto the stone. Dampened paper will pick up more detail from the stone and requires less ink and less pressure.
There is a wide range of papers that can be used for lithography including those with heavy textures and heavy weights.
As with other forms of printmaking, the most desirable papers are mouldmade as they will be more consistent and stable and more evenly made.