This seems like always a tough issue to solve. There is a master thread:
Guide: Infant / lap child fares & fees for AA travel, including award & upgrades
Seems like it's possible on JL based on this datapoint using CX miles (it should be the same process):
Infant ticket on JL?
Although yes 10% of full fare
You probably want to check with Alaska too how to get an infant ticket with them for the Vancouver to Seattle segment.