Yes, I've the same problem on my 2009 Lexus 400h. The auxiliary battery (for starting) fails on several occasions. A replacement battery is over £110 as they say a standard battery for about £60 (Yuasa YBX5063 12V 52Ah 520A Silver High Performance Battery, for example) giving about 50,000 starts, will not cope long-term as this car has the stop/start system.
However, being tight, for over a year now I've kept my car going on the odd occasions that the battery fails due to having not used the car for a while or left a light on without the "ready" light position being used, is by simply connecting, via crocodile clips, a temporary small 12v battery to the car battery terminals and switching on. It works every time. I fly electric model helicopters and use my 3 cell lipo battery pack (around 11-14v and just 4 amps). I keep one in the car just in case. But, how many Lexus owners have a lipo battery?!