Should I have my lawyer business partner incorporate our company?
It's very difficult to stay objective about the interests of the company (which is the lawyer's job) if you also have a vested interest as an owner. While it may be easier for the lawyer friend to take on the steps of handling the incorporation (we have more practice with bureaucracy-speak), be clear about whether he'll receive a fee for doing so.
That said, if both of you have agreed (ideally, in consultation with your accountants) that forming a corporation is the best business entity form for your company, you could also go through LegalZoom--or another online service--and avoid that conflict altogether.
Most important, make sure you have a written shareholders agreement between you--all the more important because you have a friendship to preserve. Without question, that should be drafted by an independent attorney. Or at least get your own counsel to review what your friend drafts as your friend will not be able to properly advise you with YOUR interests in mind.
Especially if your friend's background is in an area other than business law, you'll want the company to have its own independent counsel who is familiar with the business areas you'll be facing.