If you still hunting info on this ship try this site as has info on it as follows:
JUSTITIA
The "Justitia" was a 260 ton prison hulk originally moored in the Thames between Galleons Reach and Barking Reach. She was moored there when the American War of Independence put a stop to the practice of Transportation of criminals to the former colonies. The "Justitia formerly belonged to Duncan Campbell who was appointed to supervise the work of the convicts and provided his own hulk, and also bought the old frigate "Censor" from the admiralty. The convicts were employed "to raise soil, sand and gravel from the bed of the river for the benefit of the navigation of the said river". I don't have details of the ship, or it's ultimate fate, but there is a book called The English Prison Hulks by W. Branch-Johnson, published by Christopher Johnson Publishers Ltd. which provides details.[Posted to the Emigration-Ships Mailing List by Ted Finch - 20 August 1997]
http://www.fortunecity.com/littleitaly/amalfi/13/ships.htmYou might also want to try and get this book or the set as they contain more passenger info on folks traveling on a number of ships.
Bonded Passengers to America
by Peter Wilson Goldam
Vol I History of Transportation 1615-1775
Vol II MIDDLESEX: 1617-1775
Baltimore
Genealogiacl Publishing Co., Inc 1983