From the FAQ at http://www.daysofwonder.com/en/msg/?th=22605&start=0
Q. Can the Lizardmen use the river to get from one side of the board to the other?
Q. There are some Gnome tokens on a region bordering a chasm. Can Spiderines attack these Gnomes by DIRECTLY crawling upon them from the chasm?
A. No, they need to first conquer an adjacent non-Gnome region bordering the chasm, and only then attack those Gnomes.
Q.Can Lizardmen run over the river to directly conquer a region that is occupied by Gnomes?
A. No, because it would mean that they use their Race Power to conquer a region.