def list_contains_only_integers(lst):
  """Returns True if the input list contains only str representations of digits.

  Args:
    lst: A list.

  Elements must be strings, and if any element is not a string representation of
  a digit, the function returns False.
  """
  if not isinstance(lst, list):
    raise TypeError(f"The given input {lst} is not a list")
  for elm in lst:
    if not isinstance(elm, str):
      raise TypeError(f"Element {elm} is not a string")
    if not elm.isdigit():
      return False
  return True