Your first step in writing an essay at this level is reviewing the existing scholarship on the subject. This enables you to situate your own paper within the ongoing scholarly conversation and talk about what you are adding to it. This is absolutely essential at a postgraduate level. You should use the MLA International Bibliography to find links to existing scholarship; it should be available on your university website.
For your approach, one common feminist issue is the relationship between women and insanity. This strand of feminism argues that when women rebel against the boundaries of patriarchal society, one way to dismiss the legitimacy of their attempts to empower themselves is to condemn it as a mental health problem, calling women who wanted equality or sexual freedom mentally disturbed to invalidate their desires by a sort of gaslighting. Foucault is especially important for an analysis of diagnosis and treatment of "insanity" as social control mechanisms. Also, there is another feminist argument that trying to conform to the oppressive elements of patriarchy itself injures women's mental health. Both of these are directly relevant to Lise.
Both the eccentric dress and Lise's erratic behavior can be analyzed this way. The garish clothing is an external symbol of Lise's internal conflict with patriarchy and her attempt to break free from a life she finds oppressive.
As you work on this, you also should address the problem of Lise as an unreliable narrator. Not all the people or events she experiences are actually real.