Well, this looks like Lily in 1881 - is Charles Clifton the same person as CC Robertson?
5 Victoria St, Plymouth
William Robertson 56 London Head Family Hotel Keeper
Emma Robertson 38 London St Martins Wife
Charles Clifton 15 Middlesex Son Telegraph Messenger
Arthur Douglas 6 Exmouth, Devon Son
Lily Robertson 4 Plymouth, Devon Daughter
Walter W. Robertson 1 Plymouth, Devon Son
RG11/2194 - Folio 48 - Pg 48
To answer my own question - here's the family in 1891, although Lily's age is given as 41 instead of 14!
48 Shaftsbury Cotts, Charles, Plymouth
Robertson, William M 66 City Road, London Head
Robertson, Emma M 46 St Martins, London Wife
Robertson, Charles C 25 Soho Sq, London Son PO Letter Carrier
Robertson, Lily C 41 Plymouth, Devon Daughter
Robertson, Walter W 11 Plymouth, Devon Son
RG12/1727 - Folio 92 - Pg 93
So it's not Claude, alas.
Rambler