Dress code for many airlines can be found on www.flyzed.com, in the Travel Rules section. Unfortunately, LH has not published theirs. They do have a very laxed dress code and will accept jeans in economy class.

As for bags, the only ZED carrier (that I'm aware of) that collects 1st and 2nd checked bag fees from ZED travelers is US. Others will collect excess baggage fees (e.g., more than 2 bags, overweight and over sized bags).