This recommendation was emailed in by Karen of Avoiding Milk Protein.
They are open 7 days a week from 9am to 4pm, serving breakfast and lunch all day. Their website is bare bones, but has everything you need: hours, location/map, and the full menu. This is obviously an all-vegan restaurant and thus completely dairy-free friendly.
Location: 901 NE 55th St, Seattle, WA