Is it possible to have lupus without specific markers in your lab work?

Unlikely: That would be extremely unusual. Close to impossible.

There are many marke: Usually most people with lupus have specific laboratory tests. There are a variety of markers such as ana, ds dna, sm, rnp, ssa, ssb, histone etc to name a few and there are some that are not routinely tested like su. Everyone with lupus is a specific individual with differences. No two snowflakes are the same and no 2 people with lupus are the same, even identical twins. Your tests will see.