To search for an element in the sorted list, we can use the binary search algorithm. Here's an example of how to do it in Python:
        
        def binary_search(arr, x):
        """
        Performs a binary search on the sorted list `arr` for the element `x`
        Returns the index of `x` if found, otherwise returns -1
        """
        left = 0
        right = len(arr) - 1
        
        while left <= right:
            mid = (left + right) // 2
        
            if arr[mid] == x:
                return mid
            elif arr[mid] < x:
                left = mid + 1
            else:
                right = mid - 1
        
            return -1

        l = [1000, 102, 110]
        sorted_list = sorted(l, key=lambda x: sum(map(ord, list(str(x)))))
        
        # search for the element 102
        index = binary_search(sorted_list, 102)
        
        if index == -1:
            print("Element not found")
        else:
            print(f"Element found at index {index}")

In this example, we define a binary_search function that takes in the sorted list arr and the element to search for x. The function then performs the binary search algorithm on the list and returns the index of x if it's found, otherwise it returns -1.

We then create a sorted list sorted_list using the same sorting method as before, and search for the element 102 using the binary_search function. If the element is found, we print its index, otherwise we print "Element not found".
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