Certainly the author of Lucky Jim, Kingsley Amis, has been accused of misogyny in his later works, and indeed it was difficult for him to find an American publisher in the 1970's when he was still producing popular novels in England. In Erin Jacobs' biography of Kinglsey Amis, she notes the "increasingly dark and misogynistic tone of Amis’s fiction from Girl, Twenty (1971) through Jake’s Thing (1978) and Stanley and the Women (1984)" which coincided with the dissolution of his relationship with his lover Elizabeth Jane Howard.
The reaction to his works in the 70's and 80's is partially due to greater understanding of misogyny, which may have been taken for granted in the 1950's, when Lucky Jim was written and published. Thus there does not seem to be a lot of writing about the presence of misogyny in the book. One scholarly article by Sara Delamont, writing in Social Studies of Science Vol. 33, No. 2 (Apr., 2003), pp. 315-322, contains the following quote:
Amis' description of Margaret Peel in Lucky Jim [is] a 'neurotic' character with 'tasteless clothes' and 'utter ignorance on how to appeal to a man'.
This description helps get at the heart of what may be considered misogynistic about Lucky Jim-- all of the female characters are seen as reflections of how they relate to men, and not as real people with the depth of the title character. That said, one of the conceits of Lucky Jim is that you really only see things from one perspective, so the title character's own misogyny can be seen as part of the portrait of a young man, as opposed to something meant to speak for all people.
The best way to approach this question in an essay is probably to dive into the character of Margaret, and see how the author gives her a lot of stereotypically "hysteric" aspects, going so far as to arrange a fake suicide attempt, and how that contrasts with the more full, iconoclastic character of Jim. It could definitely be seen as misogyny to make your female lead character unsympathetic and "hysterical".
The scholarly article linked below should be available through your school library, it has a lot of in-depth info on the topic.