Thanks. I replaced the battery and the charge was covered by Lexus, although I have been unable to confirm if the battery was bad (long story). In the final analysis, either the battery was bad or the charging mechanism (alternator or otherwise) wasn't working. If the former is the case, then the problem has been solved (hopefully). If the latter, either that is a significant engineering defect or I need some direction on how to keep the 12 V charged.
The question is whether the 12 v battery charges while the car is on EV mode. If the 12 V runs down after every few hundred miles, then that is not sustainable and if there is something in my driving habits (such as operating almost exclusively on EV mode) that needs to change, it would be useful to know.
In the meantime, I am getting jumper cables. Until this happened, I had no idea that these were necessary for a PHEV.