I had always interpreted Lester's motivation as being based on her perception of women not being made starship captains. And while the point has been made that her statement that Kirk's "world of starship captains doesn't admit women" could refer to her relationship with Kirk (not a bad point) there is plenty to indicate she wanted to be a captain and felt discriminated against because of her sex.
- Lester (in Kirk's body) says "Love? Him? I love the life he led. The power of a starship commander. It's my life now."
- And later: "At last I attain what is my just due. Command of a starship. All the months of preparation now come to fruition."
- Kirk (in Lester's body) says "Janice has driven herself mad with jealousy, hatred and ambition" - hatred perhaps of Kirk for not taking her with him, but the jealousy and ambition only make sense if she wanted to be like him.
- And during the hearing: "To get the power she craved, to attain a position she doesn't merit by temperament or training."
- When Lester is back in her own body: "Oh, I'm never going to be the captain."