Luke was a small business owner and the son of a small business owner! His actual class position is broadly comparable to Loralai's when we meet them - she is the manager of a hotel and is aspiring to open her own smaller hotel.
I agree about the interpersonal problems though. The difference between them is that Loralai is still voluntarily slumming it, just as she was as a chambermaid - she's a scion of the haut bourgeoisie. She was raised with the expectations of that class and all it ever takes for her to carpet bomb her problems with money is to swallow her scruples and ring her parents. And indeed the first story arc of the show is about her doing that so that her daughter can have the class based advantages she herself rejected.
There are very few workers who are prominent as characters. Sookie the chef is a skilled worker, but she is on her way into business with Lorelai. She also marries a small business owner. Jess is technically, if I remember correctly, from a family with a small business, but he is consistently treated as being from the wrong side of the tracks and is himself en route to becoming a construction worker, so he may be the closest thing to a working class character of some significance. Even Michel the concierge is a son of privilege. The town is largely stocked with (almost all warm, good hearted) small business owners, while Lorelai's parents world consists of (cold, uptight, damaged, maid-abusing) ruling class types.