Yes, he lied about being born in Quetta India when he attested for the military in 1904. He also lied about his age. He may have wanted to disguise his true identity, because he was under age. Perhaps he thought if he gave the wrong place of birth, nobody could do a check on his age. He probably did not have his parents' permission to join the military.
Many young men did lie about their age, or give other false information, when they attested, for various reasons.
Don't rely on Ancestry transcripts. Read the actual record.
All his census records give his birth in Edmonton or Enfield or Wimbledon.
His BIRTH CERT.
HARMAN, LEVI PRINCE VICTOR -
GRO Reference: 1887 S Quarter in EDMONTON Volume 03A Page 403
His mother was Rose Florence HARMAN born 13 June 1862 Surrey.
His adoptive father was Robert Henry LUCK born 8 Nov 1862 Ealing.