How do I cite my professor in my paper and in the works cited page using MLA?

The seventh edition of the MLA Handbook 2009 clearly specifies how to cite a lecture. If you wish to quote your Professor's formal lecture please refer to the following section in the seventh edition of the MLA Handbook 2009:

"Speeches, Lectures, or Other Oral Presentations (including Conference Presentations)

Provide the speaker’s name. Then, give the title of the speech (if any) in quotation marks. Follow with the name of the meeting and organization, the location of the occasion, and the date. Use the descriptor that appropriately expresses the type of presentation (e.g. Address, Lecture, Reading, Keynote speech, Guest Lecture). Remember to use the abbreviation n.p. if the publisher is not known; use n.d. if the date is not known.

Stein, Bob. Computers and Writing Conference. Purdue University. Union Club Hotel, West Lafayette, IN. 23 May 2003. Keynote address."

If, however, the lecture is not a formal one it is not necessary to either quote it in your paper or in the 'works cited' page.