Sorry, but I don't have a Joshua Adams born 6/4/1819 nor a Lorenzo Adams. My Joshua, b. 5/5/1780 in Rutland, Vermont, had two sons Joshua, one b.5/14/1815 in Bastard, Leeds, Ontario (d. 9/30/1819) and another b. 4/25/1825 in Adamsville (now Glen Tay), Lanark, Ontario.
The other six Joshua Adamses I've captured are from Simsbury, Hartford, Connecticut and the same area of Ontario.