So 9enisP was close but a little off.
The LS requires a bolt pattern of 5 x 108 (that's 5 bolts with a spacing of 108 mm). The stock wheels have an offset of +60 mm. That means that the hub contacts the wheel at a point 60 mm (toward the outside of the car) from the center line of the wheel. Most wheels have less offset than that. Some even have a negative offset. If you put wheels with a lower offset on the LS, then the wheel will be pushed out by the difference. This can cause a problem if, when the suspension deflects, the wheel doesn't go into the wheel well, but hits the fender instead. A similar issue can be caused by using a wider tire than the originals (the tire gets closer to that finder lip).
If a car requires a small offset, and the wheels you want have a high offset, you can often use a spacer which makes up the difference (special long lugbolts are also required). Unfortunately if the wheel hase a lower offset than you need, you can't adjust for that. And the bolt pattern always must be correct without exception. That is what makes finding wheels for the LS so tricky: an uncommon bolt pattern of 5x108 and a requirement for a very high offset.
I installed winter tires on 17"x7.5" wheels with a offset of 47 mm. They work just fine. This is a rather high offset for an aftermarket wheel - most of them that you will find (in 5x108 anyway) will be around 38 to 42 mm. I personally would stick to wheels with an offset of higher than 40. Some people experience rubbing with lower offsets. Of course if you change wheel diameter or tire size you should pay attention to what you are doing as well because you can easily introduce problems that way too.