Write a Python function `check_element(lst, element)` that takes in a list `lst` and an element `element`. The function should return `True` if all items in the list are equal to the given element, and `False` otherwise.
#### Example Usage
```python [main.nopy]
print(check_element([1, 1, 1], 1)) # Output: True
print(check_element([1, 2, 1], 1)) # Output: False
print(check_element([], 1)) # Output: True
```
#### Constraints
- The input list can contain any type of elements.
- The function should handle empty lists gracefully.