It looks as though he was sometimes known as Clair (perhaps because his father was also a Horace):
Clair Lulham aged 8 in Brighton in 1881, with parents Horace & Elizabeth.
Clare Lulham aged 19 (auctioneer’s pupil) in Brighton in 1891.
As Clair Lulham he gave his sister Mabel in marriage to Percy Whitton at All Saints’, Brighton, 16 Feb 1909.