It's not really a tree branch--it's my leg! Lucy doesn't really sit on laps. She prefers to sit on your leg and grips it tightly. We joke that she's pretending we are trees and our legs are the branches.
It's not much of a stretch. She does enjoy being up high in the cat trees, and before she came inside she spent hours up in our backyard tree house. We do need to keep her nails trimmed regularly, because it can get pokey!