There is no vegetarian restaurant in town. But many places will understand "Mang sawir at" and cook more or less vegetarian.
Ganga Restaurant, 284 Chaikhong road, Chiang Khan Loei 42110 (Near Wat Tha kok(Temple Tha kok)), [1]. Delicious international food, home made pizza, pasta and burger. Best fresh coffee and varieties of famous beer all over the world. The river side table are most spectacular spots in Chiang khan. Enjoy food with 180-degree panoramic views of Mae khong river. edit
Leloei, (from Chiang Kong Road take Srichiang Kan Soi 13, at the end, it is the left restaurant on the other side of the big street). Two women usually cook outside here great Thai food. They take your request for vegetarian food whit "Mang sawir at" more serious than in other places. Coordinates: N17° 53.683 E101° 39.382 30-60 bath.