-----Description-----  
This task requires writing a Lean 4 method that finds the **majority element** in a list of integers. A majority element is defined as an element that appears **strictly more than half** the number of times in the list.

If such an element exists, the method should return that element. Otherwise, it should return `-1`. The implementation must ensure that the result is either the majority element (if one exists) or `-1` (when no such element appears more than ⌊n/2⌋ times).

-----Input-----  
The input consists of a list of integers:
- lst: A list of integers, which may include duplicates and negative numbers. The list may also be empty.

-----Output-----  
The output is a single integer:
- If a majority element exists in the input list, return that element.
- If no majority element exists, return `-1`.

