"Nurturing Parent" is gender neutral. It could mean the parent is male of female. It has nothing to do with the gender of the parent but with the character of the parent. "Strict Father" is in practice also gender neutral because mothers can behave in a "strict" or authoritarian manner, so the word "Father" in this paradigm description can be misleading.
Since you haven't bothered to read Lakoff, here is a link to a web site dedicated to Lakoff's theories. The Rockridge Institue's web site is dedicated to promoting Lakoff's theories
http://www.rockridgeinstitute.org/ and here is Alternet's Interview of Lakoff and his theory "Inside the Frame"
http://www.alternet.org/story/17574.Lakoff on what is a "Nurturing Parent" (from Alternet interview)
The "Nurturant Parent" model goes like this: It assumes that there are two parents involved and in charge of the family. And it has a set of background assumptions: that the world can be a better place, that it's our job to make it a better place, that children are born good and need to be made better, and that the job of a parent is to nurture his or her children, but also to turn those children into nurturers themselves -- nurturers of others.
Now what does it mean to be a nurturer? Well, two fundamental things. First, empathy. The parent has to know what all those cries mean when a baby cries. Does he need his diaper changed? Does she need to be fed? Second, responsibility. A parent has to be responsible to a child. And you can't be responsible to someone else if you're not responsible for yourself. You have to be able to take care of yourself to be able to care for someone else. Being responsible means being strong, being competent, being educated -- taking your role very, very seriously. If you want to turn your child into a nurturer, then you want to make that child responsible to others, strong, capable, educated, competent, and so on. Then there are other values that follow from empathy and responsibility. One of them is protection. If you're responsible for a child, and you care about the child, you want to protect her or him.
Looks like Lakoff is saying that males can be nurturing parents as well as females. He is right. Males can go against the patriachal taboos and behave in a nurturing.
You must be of the "Strict Father" mentality, who associates nurturing with weakeness and women with weakness, so that in your view nurturing = women(mothers). That is the typical patriarchal word association.