He knew the trick wouldn't work against Obi Wan. (see episode II)
So he decided to surprise obi with a new technique. And Obi fell for it with open eyes. Dooku chokes him and then throws him away. (I still dont understand why he didn't threw him on his saber, but thats another question). After that Anakin engages him and he is too busy with his saber to use some lightning. And then he dies..
Theatrically, it would have detracted from Palpatine's use of Lightning.
Story wise, lightning would have been pretty useless during an intense lightsaber duel. The three opponents that Dooku used it on in AOTC, Anakin was charging towards him from across the room, leaving him ample time to perform his trick, Obi-Wan was circling him from a distance and then blocked it with his lightsaber, and Yoda was also across the room.
It wasn't that Anakin couldn't block it; in AOTC, he was caught off-guard, and expecting to start a lightsaber duel, not be thrown aside by lightning.