Do you have to have cured yourself of Lycanthropy to get Vilkas and/or Farkas to ask to be cured?

No. Just keep a Witch head in your inventory when you talk to them about work.
Sometimes you'll need to do a few radiant missions before they ask you.

DO FARKAS FIRST!

I don't know if any of the patches have addressed this issue, but the Purity quests can really glitch out on you if get one from Vilkas first. If you want to cure both the twins, just keep going to Farkas for work until he gives you his Purity quest. Finish that and then start asking Vilkas for work until you get the quest to cure him.

Thanks.

Of course I'll do Farkas first. He's my husband, after all.