Walkthrough

Tree: $1$ has children $2, 3$. Node $2$ has children $4, 5$. Query: LCA$(4, 5)$. Both have $depth = 2$, so no initial jump. Check up[4][1], up[5][1]: both are $1$ (same), so do not jump $2^1$. Check up[4][0] = 2, up[5][0] = 2: same, so do not jump $2^0$. Wait, they are already at the same parent. Return up[4][0] = 2.

LCA is $2$. Since both nodes share the same parent, the algorithm finds it immediately.