Why Lily? May be the solution can be found here:

http://de.wikipedia.org/wiki/Madonnen-Lilie

quintessence:St. Joseph is defined through Mary and Susanna (Book of Daniel: hebr. hebräisch Shushan = Lily) is often seen as a precursor of Mary.

I have no answer and I didn’t found confirmation of a patronage. Even not here:

http://www.newadvent.org/cathen/01538a.htm

But since St. Anne has become the most popular saint in the middle age, it might be only a group of equestrians who declared St. Anne as their patron.

Or it is a misinterpretation of a picture like this:

http://www.paintedchurch.org/slapeloi.htm

The classic patrons of equestrians are St.Martin or St. George.

I found related information here:

http://de.wikipedia.org/wiki/Madonnen-Lilie

quintessence: The lily is actually related to Mary (and St. Joseph is defined through Mary) as a symbol of purity and is deduced from Sussana ( apocryphal addition to Book of Daniel hebr. Shushan = “Lily”) as a precursor of Mary, if you will.