Can my out of state immigration lawyer apply for my work permit?

Yes. An immigration lawyer may be licensed in any state and practice immigration law. It is federal law. Thus, as long as they are licensed in a state, they may process immigration in other states as well. Best of Luck.

A lawyer admitted in any jurisdiction in the US is authorized to practice immigration law since it is federal practice.  But, of course, it has to be an attorney that is familiar with the practices of immigration so that you are getting the benefit of a knowledgeable attorney in this matter.