Good Queen Bess, Gloriana, The Virgin Queen
There are many nicknames for the Queen of England. Some of these include Her Majesty, Elizabeth II, as well as Lillibet.
Her Majesty Queen Elizabeth does not have nicknames.
Lizzy is already a nickname. It is traditionally a short form of Elizabeth / Elisabeth.
Elizabeth Imus goes by Elizabeth Imus-Zero, and Elizabeth Zero.
Elizabeth Coyle goes by Liza.
Elizabeth Schell goes by Lizzie.
Elizabeth Spaetzel goes by Liz.
Elizabeth Sampson goes by Sam.
Elizabeth Sepulveda goes by Beth.
Elizabeth Vellozzi goes by Lizzie.
Elizabeth Reiners goes by Beth.
Elizabeth Wittelsbach goes by Elle.