You'll get laundry services in Lukla and In Namche Bazaar. It's more expensive than city areas but it's fortunate to get Laundry service in the Himalayas. Beyond Namche Bazaar, you'll not get any laundry service. But you'll get a running water tap where you can hand-wash your clothes if it's really necessary. Otherwise, it's better to have laundry in Kathmandu than in the mountains.