The recursive LCA teaches you a pattern: propagate results from children to parents and combine them. Each node asks its children "did you find anything?" and makes a decision based on the answers. This bottom-up flow is common in tree algorithms.
You also see that returning early (when you find a target) prunes the search. You do not need to explore the entire subtree below a target node. This pattern applies to other tree problems: find the diameter, check if balanced, or compute subtree sums. In each case, you gather information from children, combine it at the current node, and pass it upward.