Without the professor who you are their materials? No, they would need to be included on the paper for a few reasons (you can still be lead author). First, why would they use their resources and lab space with no compensation? Unless you're paying them out of pocket the only compensation is authorship. Second, you might argue that you could provide them free labor on the side for their projects, but that means you're now a lab member and as a member of the PI's lab they are entitled to be on the paper since they are supervising you. Third, pedigree matters. The reason a professor needs to be on the paper is the fact that they are putting their name out there by saying that the manuscript conveys data that was honestly collected and that it was done in a scientifically valid way. They are essentially putting their name and their degree at stake by doing so, which gives a level of authority that can't be equaled by a student with no degree, no lab, and little to nothing at stake. That being said, I have seen a medical student once publish a case report with no senior author. It always struck me as bizarre because clearly there were others involved in the care of the patient, and it is somewhat dishonest not to include the attending who actually was responsible for the clinical outcome...