I put Si wheels on my '06 LX so here ya go...
Yes, You need new lug nuts, the LX ones are for wheels with hub caps. I'm using the stock Si lugs
Yes, You will need to create some space (really small) between the wheels and the brake calipers. You can do this with spacers or you can grind down a bit of the calipers. Some people have even just put 'em on and let the wheels grind down the caliper a little bit.
I went ahead and had a friend of mine grind down the calipers on mine and it worked great. If you have the tools, this is the best option IMHO.
Here are some pics of the calipers after we took the grinder to them:
We also coated the bare metal with some rattle can clear coat to prevent rust. They still look shiney just like the day we did them.