Longest Common ancestor in tree in O(n) time

#### This issue is about [Algo/DS Name](link to resource for the Algo/DS).

- [ ] Issue Title is in form `Algo/DS Name [Language]`.
- [ ] I searched or browsed the repo’s other issues to ensure this is not a duplicate.
- [ ] This Algo/DS is worth adding to this repository.
- [ ] Assign this issue to me (I want to work on this).
- [ ] I ensure that I am not already assigned to 2 or more issues.
- [ ] I will send my PR only after I'm assigned to this issue by any maintainer.
- [ ] I understand that I will be unassigned from this issue if I fail to send a PR for this within a week.

No source file, test, or entry point is named. Start by reviewing the repository’s existing tree and algorithm implementations, then identify the expected location and conventions; done means adding the requested O(n) lowest-common-ancestor implementation with coverage consistent with nearby work.

Written by the indexing model from the issue text.