The Yamaha A1010 can drive 4 ohm speakers (two, in front), it says so in the manual, in fact (they say you should put it on a 6 ohm setting and it will run 4 ohm speakers). However, I agree with others here that using a real external amp is a good idea. I doubt a super low end amp will be any better than the A1010 directly driving it (especially since you can bi-amp the front speakers with the A1010, and that should give quite adequate power)... but I personally am driving my Lsi9's with an NAD C 326BEE amp ($550) which is rated at 50 watts/channel but in reality can burst up to 100 watts/channel and it sounds incredibly good with the Lsi9's. The A1010 has a nice clean preamp output that works well with the NAD.
I've read really good things about Yamaha's own integrated amp, the A-S500, and WhatHiFi came out with a stellar review. I can't vouch for it myself, though; I listened to it at J&R and it sounded quite blah --- but that's probably because J&R's listening room was set up really badly, with poor wiring, speaker connections, etc. The NAD on the other hand I auditioned at an audiophile shop and it sounded truly awesome --- so I got one brought it home hooked it to my A1010 and haven't looked back.
I should try hooking my Lsi9's to my A1010 in biamp mode just to see how the A1010 fares driving these speakers without the NAD. But the NAD/Lsi9 combo is truly spectacular and I doubt the A1010 alone is going to really be at the same level.