Castrol Purple Stuff will do the trick. Spray it on, let it soak for a moment, then with a wet scrub brush and a wash bucket scrub the tires. When you're done they will look like new and there should be no more lube on the tires. That stuff breaks down anythink with an oil base, just make sure you rinse very good. I normally rinse while rubbing down the tire with my hands just to make sure all the soap film is off.
Beware, Purple Stuff can make a mess of your hands. Be sure to wash them well and use a good lotion afterwards. It will eat the oil right out of your skin if you're not careful.
....and no, it will not hurt the tires. I've been using the stuff for years as well as most people I know.