The Hiram M. Chittenden Locks, built in 1911 and often nicknamed the Ballard Locks, provides a link for boats between the salt water of Puget Sound and the fresh water of the Ship Canal, which connects eastward to Lake Union and Lake Washington.
That would be how they got the ferries that were built outside of Lake Washington to the lake, but there was no ferry service through the canal. Besides, all ferry service on the lake stopped, with the building of the floating bridges, 11 years before the trip from Vancouver that you describe in 1961.