Sounds like a bearing or bushing needs to be lubed, swingarm pivot bolt, seized rear hub bearings, shock linkage/pivots. Also I have seen brake discs, most of the time the rear warped/bent just enough not to notice while riding and every time it goes around the high spot makes the brakes sqeak alittle. Some bikes have chain rollers that sound like that as well, but I don't remember if the LTZ has one or just a slider.
I don't know what year the bike is, but I know Suzuki and most manufacturers are pretty liberal about the grease they put on the bikes and the dealer during prep does not even touch these areas because they are already almost completly assembled when they get them. Just grease all the pivots/bearings and see if that helps.
Good luck.