from functools import reduce
from typing import List


def calculate_binary_or(lists: List[List[int]]) -> int:
    """
    Calculate the bitwise OR operation across all elements in a list of lists.

    This function performs the bitwise OR operation on each sublist in the given list of lists.
    Then, it computes the bitwise OR of these individual results to produce a final aggregate result.

    Args:
        lists (List[List[int]]): A list of lists, each containing integers.

    Returns:
        int: The result of the bitwise OR operation across all elements of the sublists.

    Examples:
        >>> calculate_binary_or([[1, 2], [4], [8, 16]])
        31  # Explanation: (1 | 2) | 4 | (8 | 16) = 3 | 4 | 24 = 31
    """
    or_results = [reduce(lambda x, y: x | y, sublist, 0) for sublist in lists]
    final_result = reduce(lambda x, y: x | y, or_results, 0)
    return final_result
