The same thing happened to me just after I bought my IS300, with a multimeter the battery would read not bad ( just above 12 volts) but when I tried to start the car it would turn over but reluctantly but started then if I left anything running without starting the car I got the clicking .
Took it back to the garage and they said the battery was ok as it was reading over 12 volts, forced the garage to send it down to there Lexus branch as I only had the car 4-5 weeks and the lexus boys replaced the battery and it has been cool since. :D