Write a Python function `count_integer_elements(lst)` that takes a list `lst` as input and returns the number of integer elements in the list. The function should count only elements of type `int` (not `float` or other numeric types).
#### Example Usage
```python [main.nopy]
print(count_integer_elements([1, 2, 'abc', 1.2])) # Output: 2
print(count_integer_elements([1, 2, 3])) # Output: 3
print(count_integer_elements([1, 1.2, 4, 5.1])) # Output: 2
```
#### Constraints
- The input list can contain elements of any type.
- The function should not count elements that are not of type `int`.