I was looking to see if anyone else has input on this and share my experience so far as it doesn't match what I had seen in previous posts. I had initially called JAL to see if I could add the lap infant, they had said Alaska handles everything. Called Alaska who was able to add the lap infant without issue - I can see the the lap infant added in both Alaska and JAL site (where I can select seats as well).
I was fully expecting to pay 10% of the Premium Economy fare, but Alaska said it was just a $18 fee and confirmed with me that I did not need to call JAL for anything else. To me it seems to be all set but at the same time, all the previous posts I saw JAL should have been the one to add the lap infant and collect the 10% fare (which should be way more than $18).
Maybe their process has changed and people can use this as a data point.