I had a 2001 IS300 with 105K miles on it. The car had the same problem as you described. I recently replaced the spark plugs but it still cranked more than usual before it start. Then couple months later...one morning the car didn't started at all. Tow truck gave it a jump start and it started just fine. The moment I put the car into D gear, it stalled. He did some test and convinced me that the alternator is dead. Therefore, it didn't charged the battery. Needless to say, the combination of bad alternator and old battery (more than 4yrs) will strain you in the middle of nowhere. Take the car to the shop and have it test by the professional. Good battery (700 cold AMP) $110 and a rebuild alternator with lifetime warranty from auto zone $150 will put at least another 5-6 years on your lexus. Good Luck. Ta.
