A slightly snobby way to describe someone who's a member of the lower middle class, particularly if they run a small business, is petit bourgeois.
Referring to people as petit bourgeois is an insult — it implies that you think they're overly focused on money, and perhaps that you find them closed off to new ideas. The philosopher Karl Marx is often credited with coining this phrase, although experts note that Charlotte Brontë was the first to use it in print, in 1832. The class of petit bourgeois people is often described as yearning after the money and power of the higher economic class.