Applications Beyond Ancestors

Binary lifting is not for ancestor queries. You can use it for:

$1.$ LCA in $O(\log n)$ per query (as you saw).

$2.$ Path queries: find the sum/max/min on a path between two nodes.

$3.$ Level ancestor: find the ancestor at a specific depth.

$4.$ Jump pointers in graphs: precompute jumps of size $2^j$ in any DAG.

The core idea (precompute power-of-$2$ jumps, then binary decompose) applies to many problems.