Today, there is no town of American Lake, though Percy refers to a place he calls American Lake that had a train depot and at least some stores. Also, the 1917 map of Camp Lewis is titled Camp Lewis American Lake, Washington
The major town on American Lake today is Lakewood. From the Lakewood Historical Society website:
"The Tacoma Country and Golf Club was established in 1894 to further attract the rich and famous.
Many stately homes were built on estates along the shorelines of area lakes, the most impressive
being Thornewood, built on American Lake between 1909 and 1911."
The golf club is still on American Lake, opposite the site of Camp Lewis.
When Percy arrived, Camp Lewis had only been established for a few months whereas American Lake had been a major recreation site for decades. Hence, Percy's reference to leaving Portland for American Lake rather than for Camp Lewis.