Plural possessive; upper case because the title is comparable to a chaired professorship.
Put the full titles of lectures in quotation marks: The subject of his lecture is “The World of Ambrose Bierce.” Topics need no quotation marks: She will speak about the fiction of Ambrose Bierce. Capitalize lecture titles and lecture series titles, but not any preceding modifiers: She delivered the fourth annual Holmes-Hunter Lecture.
Do not hypenate in any form. An exception to AP style.
For all uses. An exception to AP style.