You obviously have seen the 1881 census, and therefore know that Elizabeth was staying with her grandparents?
Connelly, James Head M 57 General Labourer b Ireland
Connelly, Mary Wife F 52 b Ireland
In 1891 Elizabeth is a servant with the Crowland family
Reference RG12, Piece 2884, Folio 97, Page 41
I think this her marriage:
December qtr 1892
Liverpool district Vol 8b, Page 188
Connelly, Elizabeth
Pearson, James
Because, checking all the potential grooms against 1901, this is them (I think!):
Reference RG13, 3433, 85, 2
Greystoke The Stables, Aigburth Drive, Toxteth Park
Pearson, James Head M 29 Coachman (Domestic) b Birkenhead
Pearson, Elizabeth Wife F 29 b Birkenhead
Person, Ralph Son M 5 b Blundellsands
Pearson, Arthur Son M 1 b Liverpool
Pearson, Violet M Daughter 1 month b Liverpool