They are in the 1871 census and children's birth places and ages indicate that Lawrence and Frances were overseas at the dates of the 1851 & 1861 census.

Back Strand Douglas RG10/5775 p. 20
Lawrence White 43 Labourer b Co. Kildare Ireland
Frances 40 Co. Kildare Ireland
Wm. son 17 Carver & Gilder Draughade? Ireland
Geo. 13 Scholar b. Corfu
Augustus White 10 b. East Indies
Eliza 5 b. Douglas
Robt. 3 b Douglas
Elizabeth 1 b Douglas

Note that in 1881
67 Duke St. RG11/5604 p. 11
Frances E White Mar. Wife (Head) 49 b. Douglas
Edward G. son 23 Stone Mason b. Corfu
Laurence A. 21 b. Stone Mason b Kerrucher?East Indies
Eliza 15 b. Douglas
Robt. H. 13 b Douglas
Frances E. 11 b Douglas
Sarah M. 7 b. Douglas

Rushen Gaol of Castle Rushen RG11/5607 p. 2.
Laurence White 55 Married. Prisoner. Retired Army Private. b. Co. Kildare