A search on freebmd came up with a birth registered in June quarter 1838
Elizabeth Oxby Grantham 14 page 374
The registation district of Grantham spans the borders of Lancashire and Lincolnshire. The only way to find out if this is your ancestor is to get a copy of the birth certificate. With the information above you can get them directly from the GRO - information available on:
www.statistics.gov.uk/registration/
hope this helps