Character Analysis
Lin doesn't show up until Act 2 of Cloud 9. But once she does, she's a central character and we learn three important things about her.
The first thing we learn about Lin is that she's definitely not ladylike in any conventional way, as we realize when she tells her daughter Cathy to paint, "a car crash and blood everywhere" (2.1.23). She's not exactly pushing the traditionally girly dolls n' flowers angle.
The second thing is that she "hate[s] men" (2.1.109). It's pretty obvious where this hatred comes from, considering that the only thing she's grateful for about her previous marriage is that her husband "didn't hit [her] harder than he did" (2.1.103).
Third (and most importantly for the plot of Cloud 9), Lin likes girls. She has a crush on Victoria and wants to have sex with her.
By the end of the play, Lin agrees that she, Victoria, and Edward should all live in a house together and that Edward should mind the children. Of all the characters in this book, Lin is probably the most aggressive when it comes to breaking away from predefined gender roles. The problem is that she's so obsessed with breaking away from gender roles that she sometimes forces her daughter Cathy to conform to her ideas of nonconformity.
For example, Lin says, "You'll have a smack" when her daughter Cathy tries to doll herself up with "ladylike" clothing (2.1.241). In this case, Lin hasn't solved the problem of gender roles. She's just turned everything on its head and is trying to force her daughter not to conform. But what Churchill is saying in this play is that it's wrong to force anyone to be something other than what they really are.
Lin's Timeline