Doug,
No, sockeye don't normally spawn in lakes. Sockeye can spawn on gravelly lake beaches, but only in areas where a constant source of fresh (surface or spring) water percolates through that gravel, and you can imagine how rare that circumstance is. That said, there are a couple of Lake Washington beaches where sockeye do successfully spawn. The vast majority of sockeye spawn in rivers and streams (as most of the Lake Washington sockeye spawn in the Cedar River). Large runs of sockeye only occur in river systems that have lakes in them, though many rivers have small populations of so-called "creek sockeye". The lakes are necessary because the typical life cycle of the sockeye seems to require that the newly-hatched fry swim up or down to, and live in the lake for one to two years before migrating to the ocean.