Hi Dawn,
I have never heard of a Lucas distributor being used on a Dragonfly. Most of the common Lucas distributors turn clockwise (looking at the points plate) whereas a Dragonfly turns anticlockwise, so the auto advance probably wont work - and if it did, it would actually auto retard!!
Probably, the best solution to the Miller problems is to have a new distributor body machined up that will take a Lucas points plate. You can then use a twin points set up (as on a Norton Commando, etc.) firing twin coils if you intend to retain the 6 volt system - or just substitute a Boyer pickup assy if you want to go down the electronic route and convert to 12 volt. With the electronic setup, the advance is built into the electronics, so a fixed cam can be used. If sticking with the 6 volt points system, the main spindle will have to incorporate an advance system.
Back in the 80's, I converted my Dragonfly to twin points and coils (still on 6 volt) using the original Miller advance bobweights attached to a custom drive shaft that runs on 2 needle roller bearings. the points cam is a copy of the profile used on a Tiger Cub, but modified to suit the new shaft. The twin points plate is from a unit Triumph which should run clockwise but seems quite happy running anticlockwise! This setup runs quite happily for in excess of 15,000 miles at a time without any attention to the points - however, I have mounted the condensers on the ignition coils where they get a good blast of fresh air (I'm convinced they get cooked in their original position under the engine cover).
There is another option - to use a twin output coil and do away with the HT side of the distributor - but beware, these coils don't have 2 windings - they are wound with an HT lead on each end of the secondary winding, so they rely on having a full circuit from one plug to the other to operate - if there is a fault on one cylinder, it could cause both to cease operating!
Hope this is of some help,
Regards,
Eddie.