Just wanted to add my two cents worth 
I have a fairly high end computer, 8 Gb DDR2 and a Quad core processor, got a GTX 275 1.5gb gfx card.. and the lol Client is owning my computers face. Sad, sad but true. The issues with the LOL client only occur AFTER my first match, although i see no significant Performance hits during the game, Running max settings, hitting 60 fps still, i used to be uncapped pushing 80+ fps and now i have to set in game options to stabilise at 60 to keep it from being choppy, and it falls below 60 sometimes 
After the First game however.. Lol client is near on un-responsive, delay in response from key commands when typing in chat, delay trying to switch menu screens ( home page to summoner profile, ETC) and while starting games, Sometimes my Team chat is completely unresponsive. changing masteries and summoner spells? no chance. and even sometimes.. and only sometimes. Character selection is out of the question. I'm ashamed that my beast of a machine that can tear through games like borderlands and cod 4 and pretty much every other game on the market at max settings.. Gets taken to school by the lol client.
There has to be a memory leak somewhere for it to be chewing up a Quad core processor.
i'll attach my Dx diag files and if i can find my Air logs i'll post them too
All i can say is, i'd regret to have to play on my laptop
because it would be like kicked in the groind from behind. unaware it was about to happen... with all my friends watching.
hope you can find the issue soon 
P.s. It is definately something to do with the lastest patch, my laptop has suffered severely from the most recent patch. No chance to play on the go anymore
(
P.s.s Disabling menu animations at log in, increased the performance of the client on First run for me. After first game it was back to BS. cheers.