I don't really think mixing a Sweeper set with a bit of support is good for a Pokemon like Anorith. It's got 95 base Attack and base 75 Speed, so a sweeper with some kind of buff would be better.
Honestly, I'd replace Cross Poison too. Poison-type attacks aren't as effective in LC as they are in a Metagame like NU.
Here's a moveset for a sweeping Anorith:
Rock Slide (STAB)
Brick Break (Breaks down screens, and omits two important weaknesses)
Swords Dance / Rock Polish (More Attack or more Speed? I, for one, like Rock Polish more, but it's a choice right)
Sandstorm (Set up a nice hazard for your opponent)
Rapid Spin (Spin away opponent's hazard)
Stealth Rock (Use your own hazard against the opponent)
Rock Slide / X-Scissor (Choose your STAB)