You really could do with either Sarah or Mary Anns birth certificate to confirm Elizabeths maiden name. I have a strong feeling that it wasn`t Lazenby.
On the 1851 census there is an Elizabeth Jackson aged 19 a servant born Peathorn Yorkshire (one site has it as Yorke Peathom) living in Newton Manchester. I rather think it is your Elizabeth.
Manchester Cathedral
6th March, 1853
John Pilkington, 22, Bachelor, Stoker, 5 St, Johns Terrace, Longsight, father Richard Pilkington, Farmer
Elizabeth Jackson, 23, Spinster, 5 St, Johns Terrace, Longsight, Father Thomas Jackson, Farmer
John signed Elizabeth made her mark
Christ Church, Heaton Norris
24th June, 1860
Henry Jones, Full Age, Bachelor, HAMMERMAN, Heaton Norris, father John Jones, Carpenter
Elizabeth Pilkington, Full Age, WIDOW, Heaton Norris, Father Thomas Jackson, Farmer
Henry signed and Elizabeth made her mark
Witnesses were John and Eliza Wilson.
Mo