Specify strict ‘order by’ in WordPress query

You could use usort(). Your callback function would need to determine the last names and sort by them.

So, for instance:

$args = array( 
    'post_type' = 'Employees',
);
$employees = get_posts( $args );
usort( $employees, 'wp91501_sort_employees' );

and then your callback might be:

function wp91501_sort_employees( $a, $b ) {

    // split the names into arrays
    $a_name = explode( ' ', $a->post_title );
    $b_name = explode( ' ', $b->post_title );

    // get the last name from the $x_name arrays
    $a_last_name = end( $a_name );
    $b_last_name = end( $b_name );

    if( $a_last_name == $b_last_name ) {
        return 0;
    }
    return ($a_last_name < $b_last_name ) ? -1 : 1 ;
}

Note that this is a very simple comparison — if the employee has a double last name with no hyphen (for instance, “John Smythe Jones”) then it’ll get sorted according to the very last part of the name (in the example, “Jones”).

An easier option might be to enter the employees in the form ‘LastName, FirstName’, which would allow you to just sort by post_title ASC. But then you’d need to filter the_title if you wanted to display the title as ‘FirstName LastName’.