Treat a lambswool mitt as you (or the wife would) a lambswool sweater - gentle soap flakes, hand wash, drip dry. Synthetic mitts of all types can go in the wash, on a 40 degree setting, but no tumble dry - surely you're not in such a hurry ?
I got a lambswool one from Race Glaze at £9.99, which is superb, and is wool both sides. I upgarded from a simulated (i.e. fake) sheepskin one from them at about £6 which is now for my wheels - thats still fully intact after 2 years. I do like their products and personal service.