Westlake Station

You can use Google map to do a quick search

you should try to get to the Westlake station, then take the southbound train all the way to Sea-tac Airport Station

Take the south bound link rail towards Angle Lake. The airport is a the stop before Angle Lake.

No lockers in any of the stations. They are all a single purpose transit station. No lockers, no restrooms. Westlake does have inside entrance to some downtown department stores.

Light Rail Transit states that "Service is available from 5 a.m. to 1 a.m. Monday through Saturday and from 6 a.m. to midnight on Sunday and holidays."

There's a free Waterfront shuttle that's runs from downtown to various stops on Waterfront. Not sure of their route. Can also walk, rideshare/taxi down there. If you are staying down there or going on a cruise they usually have Van's at the airport.

I think you can do a quick search on Google map where it shows you the directions