Given a list of vertices in a binary tree output minimal sublist with the same lowest common ancestor
Consider your binary tree as a binary search tree on the integers $1$ through $n$ to find that the answer for some given list $L \subseteq [1, n]$ will be $\{\min L, \max L\}$. In case you are not given a BST, you can traverse the given tree in-order to find those values in linear time (though that might be dependent on the data structure used to store $L$).