Write a Python function `find_max_length_element(lst)` that takes a list of lists as input and returns the sublist with the maximum length. If there are multiple sublists with the same maximum length, return the first one encountered.
#### Example Usage
```python [main.nopy]
print(find_max_length_element([[1], [1, 2], [1, 2, 3]])) # Output: [1, 2, 3]
print(find_max_length_element([['A'], ['A', 'B'], ['A', 'B', 'C']])) # Output: ['A', 'B', 'C']
print(find_max_length_element([[1, 1], [1, 2, 3], [1, 5, 6, 1]])) # Output: [1, 5, 6, 1]
```
#### Constraints
- The input list will contain only lists as its elements.
- The input list will have at least one element.