Thanks for the response, travellerK.
In case anyone runs into this, here's what happened in my case.
I called United again and after an hour the agent said the infant's ticket was queued and to call back in 24-48hrs to find out what the fees were. I also requested that since I was still in the 24 hr window and could cancel the award without a fee, I wanted to extend that until the time I could find out the infant's fee.....in case it would be better economically to buy the ticket without award mileage. And she verified it with her supervisor. (I didn't want to be hit with the $150 award redeposit fee)
I called UA back 48 hrs later and was on hold for another 1.5 hrs (ugh). They gave me a confirmation code for the infant and the charge was $574.10 for the infant in lap ticket.
Since this was an open jaw ticket, I thought it might be cheaper to try a RT award LAX --> BKK but the fees on the website was $528.30 (including the $65 fee for the adult). I called Thai Airways to see how much they would charge directly and it would be $503.40 just for the infant. So that wouldn't save me anything. Oh well. At least the baby has a confirmed ticket reservation #.