The way to use data with Custom Polygon's is to keep the Polygon File and Data File seperate, and then blend them.
So for example your polygon file would just hold the LAU Name, Points, Coordinates (Long/Lat), and Plot order. Your data file would contain a list of all the LAUs with, say, population (or any other measure you have). It's important that the LAU name match in both data sources (and it makes life easier if they both have the same column name but you can get round this by manually editing relationships).
You then create the Polygon's as you have done (having this as your primary data source), and then drag the population field (from our example) into the colour field, and you should now have your LAUs colored by population.
Hope this helps, and I have understood your issue, but if not please post back.