William Giles was born out of wedlock before his mother married John Lamb.
FreeReg.org.uk Baptism entry https://www.freereg.org.uk/search_records/58187650e93790eca325a6d5?search_id=5b29401b791e3bdbbca754bd&ucf=false
"Field: Value; County: Nottinghamshire; Place: Oxton; Church name: St Peter and St Paul; Register type: Unspecified; Baptism date: 10 Nov 1770; Person forename: John; Father forename: John; Mother forename: Hannah; Father surname: LAMB; Person abode: Oxton; Transcribed by: Holly Brown; Credit: Holly Brown; File line number: 1714."
FreeReg.org.uk Marriage entry https://www.freereg.org.uk/search_records/58184e1de93790eb7f8d924f?search_id=5b2941a6791e3bdbbca75645&ucf=false
"Field: Value; County: Nottinghamshire; Place: Lowdham; Church name: St Mary the Virgin; Register type: Phillimore's Transcripts; Marriage date: 11 Jan 1802; Groom forename: John; Groom surname: LAMB; Groom parish: Oxton; Bride forename: Ann; Bride surname: GILES; Transcribed by: Hilary Jarvis; File line number: 308."
Have you taken a DNA test? If so, login to add it. If not, see our friends at Ancestry DNA.