Perhaps the earlier Florentine Lille already depended on the French Lille ... the Anjou, which manifested in Italy in the second half of 13th century had friends in Florence.
The link I gave earlier, http://www.thatsflorence.com/discoverin ... -florence/
, says that the Florentine lily dates back to the 11th century. That seems plausible to me, as the Ghelph/Ghibilline struggles were before the Count of Anjou made his deal with the Pope to intervene on the side of the Guelphs in return for most of the spoils. After Manfred, defender of the Ghibellines (who got back in power in Florence and everywhere else), was defeated at Benevento in 1266, followed by Conradin in 1268, the French army occupied Northern Italy, Ghibillines were slaughtered, their property burned or confiscated. and it was all over (see http://en.wikipedia.org/wiki/Manfred,_King_of_Sicily
for some of this).
I don't know anything about the rest of what you say.
German wiki says ...
Der Name Ghibellinen / Waiblinger ist für das mittelalterliche Italien die Bezeichnung für die Parteigänger des Kaisers, benannt nach der heute württembergischen Stauferstadt Waiblingen und dem Kampfruf der Staufer. Die Existenz dieses Namens ist erstmals um 1215 zur Zeit des Stauferkaisers Friedrich II. bezeugt.
The name Ghibellines existed since 1215, according this. The name Welfen (= Guelphen) is older ... in 12th century Henry the lion (Welfen party) had conflicts with emperor Fredrick Barbarossa, a Staufer. This conflict might have proceeded to the later Italian conflict Ghibellines/Guelfs.
The link, that you gave, doesn't speak of "11th century" .... ?
11th century would be rather early for "heraldic devices", though the lille in France seems to be rather old as a symbol.
German wiki: Florentiner Lilie
with lots of examples
The Florentine Lille differs in color and by "Staubfäden" from the French Lille.
Perhaps we should look for examples of the Medici device (six palle with Lille) around 1465. Either they are with "Staubfäden" or not.
One palle is blue, the other 5 red. "Blue" associates France, one should assume. I don't see "Staubfäden".
http://www.theflorentine.net/articles/a ... tocId=7605
... subtitled "The augmented coat of arms granted to Piero by Louis XI in 1465, replacing one of the six "balls" or palle of the family arms by a somewhat larger ball showing the arms of France." at ...
It's a French Lille, not a Florentine Lille, no doubt, I would say.