Lowest Common Ancestor in Binary Search Tree Given Two Values

Problem:
Given a Binary Search Tree (BST) and two values, find the lowest common ancestor.

Note:
Two values are given in this problem, instead of two nodes. But the idea should be similar. Here I am giving two options: one is to find the node first and then search by node, and the other is to directly search by value. However, these two are the same in nature: comparing by value and validating the nodes.

Assumption:
The values are distinct in the BST. If not, the problem will become complicated. Consider the BST with all equal values in nodes.

Complexity:
Average case? Worst case?
For BST, balanced or unbalanced? Need to take this into consideration.

Solution 1:
Find the nodes first and then search by node.


Solution 2:
Directly search by value and then validate the values.