Bremerton-Kitsap Airporter operates a bus from SeaTac to Fort Lewis hourly. Tickets cost $15 - $22 and the journey takes 1 h 15 min.
How to get from SeaTac to Fort Lewis
From SeaTac Airport, WA bus to Madigan Hospital Nursing Tower. 1 h 15 min $20. From SeaTac Station bus to Lakewood TC - Zone C then line 206 bus to Madigan Army Hospital Bldg 0948. 2 h 19 min $4. From SeaTac taxi to Fort Lewis. 50 min $278. From SeaTac drive to Fort Lewis. 50 min $4. From Seattle Airport towncar to Fort Lewis. 49 min $130.