The censuses suggest there were no family links with Lincolnshire. Henry just happened to be working there.
1861
The Rectory, Yarborough
Henry LLOYD 45 Rector of Yarborough, Yorks Hornby
Ann Elizabeth 38 India
Alicia Margaret 2 Yarborough
George Wm 1m Yarborough
plus servants
1871
Fairlawn House, Northam?, Herts
Anne E LLOYD 38 Clergyman's Widow, India, Brit Subject
Alicia M 12 Scholar, Yarborough
George W 10 Lincs Scholar, Yarborough
Henry J G 8 Scholar, Yarborough
Jemima BEAUCLERK (vis,wid) 54 Widow of Duke's younger son, Scotland
plus servants
It looks as if all the kids were registered as LLOYD rather than LLOYDS.