Lowest common ancestor of a binary tree (not a BST)

def lowestCommonAncestor(self, root, p, q):
        """
        :type root: TreeNode
        :type p: TreeNode
        :type q: TreeNode
        :rtype: TreeNode
        """
				# If looking for me, return myself
        if root == p or root == q:
            return root
        
        left = right = None
        # else look in left and right child
        if root.left:
            left = self.lowestCommonAncestor(root.left, p, q)
        if root.right:
            right = self.lowestCommonAncestor(root.right, p, q)

        # if both children returned a node, means
        # both p and q found so parent is LCA
        if left and right:
            return root
        else:
        # either one of the chidren returned a node, meaning either p or q found on left or right branch.
        # Example: assuming 'p' found in left child, right child returned 'None'. This means 'q' is
        # somewhere below node where 'p' was found we dont need to search all the way, 
        # because in such scenarios, node where 'p' found is LCA
            return left or right