First of all I want to comment on the statement that Aradia is the Goddess worshiped in Gardnerian Wicca. The names of the God and Goddess in Gardnerian practice are oathbound and only given to those who have been properly initiated into Gardnerian practice. So if one makes a claim to know the names of the God and Goddess in Gardnerian practice who has not been initiated then it is likely that they are mistaken. Or if they have been properly initiated and taken oaths to never reveal the names of the God and Goddess they must be oathbreakers.
In addition, Lucifer was not a sun god. He was the God of the morning star and considered to be the brother and then consort of Diana.
That being said, Aradia is the central Goddess figure both in forms of Italian traditional Witchcraft and also in "Stregheria" which is a mishmash of Italian folkloric Witchcraft and Wicca created by Raven Grimassi.
On a more academic note, it appears likely that Aradia is not a single Goddess figure but rather a composite of a number of mythological and historical individuals drawn from both pre-Christian and post-Christian Italian folklore. You can find an excellent article about her at http://www.jesterbear.com/Aradia/Aradia.html
The idea that her supposed father was Lucifer is perfectly valid. Lucifer is a Roman personification of light specifically the morning star (Venus).
In Stregheria you see Aradia venerated a lot as the witch hero you described. Also the "Witches Bible" (Gospel of Aradia) is the book written by Leland that describes her. The practices of the stregha are heavily dependent on that book.
In my opinion Aradia is a character made up by Leland. There is no historical reference to her not even by the Church. Generally the Inquisition kept records of "witches" and the like.