Not sure if you already have this information, but if you obtain the marriage cert' using the reference below it will have both Jarvis and Lucy's Father's names on it...
Groom's Name: Jarvis Heath
Bride's Name: Lucy Smith
Marriage Date: 03 Mar 1840
Marriage Place: Saint Phillips,Birmingham,Warwick,England
Name: HEATH Jarvis Place: Birmingham Vol: 16 Page: 320
1841 Census
Address: Holland St
HEATH Jarvis M 20 Gun Finisher Warwickshire
HEATH Lucy F 20 Warwickshire
CAIN Jas M 25 Wire Drawer Warwickshire
HEATH Matilda F 1 Warwickshire