There aren't too many LCCs in the world with the same product offerings that DJ has. In fact, I'm at a loss to name one.
I believe Air Berlin and Vueling also had humble "textbook LCC" roots but like DJ have similarly evolved into "LCC with frills" carriers, or New World Carriers is the term I believe.
Southwest, Virgin America and Jetblue maybe? They have loyalty programs and VX operates a First Class. I don't think any of them operate lounges, though VX F pax are allowed to use the VS CH at SFO when flight schedules of the 2 carriers overlap.