On the principle that names on baptism can sometimes change from the registered name, there is a birth registered in Warwick registration district in the right quarter for the baptism.
From FreeBMD
Births Sep 1906
Marks  Muriel Alice     Warwick  6d 696 
However there are three other Marks births registered in Warwick 1901-1908 so I wouldn't say I find it compelling evidence.
The 1901 census does show Mercy's sister Rose (as in Mercy born Walsall) as a servant in Leamington
RG13 2932 folio 166
30 Leam Terrace Leamington Priors  Warwickshire 
Rose Marks 17  Walsall, Staffordshire,  General Servant  Domestic
as well as two other sisters
RG13 2932 folio 142
Bowling Green Inn 18 & 20 New Street Leamington Priors  Warwickshire   
Charles Duffin 38 Old Stratford, Warwickshire,  Head  Married Beer retailer
Catherine Duffin 34  Princees End, Staffordshire, Wife Married 
Hilda Duffin 7  Leamington, Warwickshire, Daughter  
Kathleen Duffin 2  Leamington, Warwickshire, Daughter  
Frederick Duffin 4mths  Leamington, Warwickshire, Son  
Hannah Markes 20 Walsall, Staffordshire, Sister-in-law  Barmaid
Marriages Dec 1892
Duffin  Charles    Walsall  6b 1145   
Markes  Catherine     Walsall  6b 1145 
I think Mercy's mother's maiden may have been Morgan
1871 census RG10 3006 folio 148
30 Albert Street Sedgley  Staffordshire   
William Morgan 50 Willington, Shropshire, Head Married labourer
Sarah Morgan 52  Tipton, Staffordshire,  Wife  Married
Thomas Morgan 21  Tipton, Staffordshire,  Son Labourer 
Harriet Morgan 17  Sedgley, Staffordshire,  Daughter   
Joseph Marks 8  Sedgley, Staffordshire,  Grandson  
Joseph was not with his parents and siblings on the 1871 census.
I suppose it could be possible that Day is Arthur's surname and Lawrence his middle name if he wished to disguise his name in anyway. However having searched that doesn't seem to throw up any further Arthur possibilities.
Regards
Valda