Hi Jo
Thanks for clarifying. Have you thought of getting your grandmother's death certificate? It may say whether she was single, married or a widow.
There are few Lucy Prices. The most likely one I have found is on freebmd, (Cheshire BMD don't seem to have got this far with their Birkenhead death index):
Lucy Price, Sept 1926, aged 46, Birkenhead, vol. 8a, page 498
Again the age may have been guessed at if her death was registered by an official working for Birkenhead Union, but it widens the scope for finding the most likely birth certificate.
I hope that helps
Fiona