This The Mentalist screencap might contain
strada, città scena, ambiente urbano, scena della via, città, urbano impostazione, istituto penale, struttura penale, istituzione penale, and penale facility.
The writers and actors don't want those two to get together. In fact, they laugh at the fan that want them to. Which personally I find a bit rude, but I won't get into that. Anyway, their reasoning for them not getting together (at least right now) is "they have più of a brother/sister relationship."
I'm sorry, but every time someone is trying to make an argument for why two people shouldn't be a couple, it's always either "they have no chemistry" o "they have a brother/sister relationship." But I've never seen anyone deny Jane and Lisbon's chemistry, so I won't focus...