Here are some other possible clues
A Paddock Lawrence was born to Justus Lawrence and wife Deborah July 1, 1767 at Barnstable. May be a clue.
Hannah Lawrence, daughter of Joseph and Betty (Paddock) Lawrence was born Sept 4, 1735. She married Seth Barlow, had several children and apparently died in Lee, Massachusetts. The source is NEHGR 172:73-4. Taking a look at Sandwich VR, she is shown immediately above Justus in the births section, children of the same parents, Joseph and Bette Laurance (sic) .
The NEHGR source for Hannah Lawrence, also cites Paddock Genealogy for her parentage ( Curfman, Robert Joseph,. The Paddock genealogy : descendants of Robert Paddock of Plymouth Colony, blacksmith and constable, 1646. Fort Collins, Colo.: Curfman, 1986.), page 48, which is available via Ancestry. Page 48 shows the same marriage that Anne found. One possible clue, though, is that it gives Joseph Lawrence's birth date as March 29, 1705; he died in Harwich in 1763, and was the son of Joseph, and grandson of Robert. Clearly the Betty shown is not correct...
Jemima Lawrence named Hannah Lawrence in her 1758 will, as the "eldest daughter of my brother Joseph Lawrance". Same NEHGR article, citing Barnstable County probate.
If nothing else, hopefully these clues can help..