Common Mistakes

Mistake $1$: Forgetting to handle the case where one node is an ancestor of the other. If $u$ is an ancestor of $v$, then $lca(u, v) = u$. Check for this after equalizing depths.

Mistake $2$: Using up[u][i] == up[v][i] as the condition to jump both nodes. You should jump when up[u][i] != up[v][i]. Jumping when ancestors match overshoots the LCA. Only jump when ancestors differ, so you stop just below the LCA.

Mistake $3$: Not accounting for $0$-indexing vs $1$-indexing. If nodes are $1$-indexed, adjust your $up$ table and $depth$ array so.