This is bizarre. I posted a reply with a sample solution and it is not appearing. Here is a sample though. Basically, I would manipulate the data in the underlying DataTable within the LookpTable. I found a simple example online that involves creating a clone of the original DataTable and re-inserting records into it backwards. Obviously, this isn't the most efficient sort, but I am not aware of a way to simply sort an entire DataTable without specifying a column to sort on (which might change your order). This solution is probably fine enough though more DataSets under 100k.
In my solution, you'll notice I seeded the DataTable from a script as this was the most efficient way to get thousands of records into the table. I also made sure to specify the DataSource after the table was seeded as many changes to the DataSet in a DataGridView tends to lock up the UI thread.