From the marriage record, Jane was born about 1836 at Boston so I had a quick peek at the city directories:
1835 - Daniel Lynch, laborer, 153 Broad
1836 - no Daniel Lynch found
1837 - Daniel Lynch, Housewright, Robinson's Lane (this address corresponds roughly to modern-day "Freedom Trail" in the area of the Paul Revere Mall)
A Daniel Lynch is also found in 1835 tax roll for Boston Ward 9 and 1837 roll for Ward 1
Only Lynch birth I have found at Boston around the right time is indexed as Mary Lynch, daughter of Mary Lynch and an unrecorded father born 1836