[sirinsidiator]

That answer in that other thread was regarding adding and removing new controls to the menu. As long as you just want to update the existing controls, that's supported.
You simply have to tell LAM that you have changed something in the data table, otherwise it wouldn't know that the dropdown choices are now different:

-- make sure you can access the dropdown via a variable name:
local optionsData = {
 --snip--
    reference = "myDropdown"
  },
}
 
-- either change the optionsData table
optionsData[1].choices = newChoices
myDropdown:UpdateChoices()
 
-- or set values independently of what is stored in the optionsData. That way you can go back to the original values later
myDropdown:UpdateChoices(newChoices)