What exactly are you looking for in "labs"? If you are looking for autoimmune conditions, then a rheumatologist IS the doctor you want.

Most immunologists focus more on allergies and immune deficiencies. There are some that work with autoimmune disease, but you need to search them out.

A rheumatologist will run a ton of labs...they are notorious for this and extended consults/exams as well. My last trip to the rheumatologist, he took 13 tubes of blood (and some were to run more then one test from same tube).