Your main aim in writing a critical essay about a literary work is to address some issue that would not be immediately obvious to someone who has read the book. Thus, a plot summary is not a critical essay, because it covers ground that would be familiar to any reader. What would count as a critical essay would be analysis of such things as what works influenced the play, the differences between the French and English versions, the relationship of the play to its historical context, or the use of literary devices in the play.
Your essay should start out with some sort of an analytical thesis. So, for example, you might talk about how Lucky's "thinking" is might have been influenced as much by Flann O'Brien's short essays as by earlier philosophers. Once you have introduced your main claim in your first paragraph, you should write a transitional paragraph pointing forward to how you intend to support your claim. For example, if talking about O'Brien's influence on Beckett, you would state that you would first provide evidence for Beckett being acquainted with O'Brien's work, then do a close reading of the relevant works by O'Brien, and finally present those elements in Lucky's speech that show this influence. Your conclusion would clarify just how the body of your work proved your initial thesis.