There are three possible marriages for him in the English/Welsh indices, two with exactly the right initials:

Name  Registration District  County  Year of Registration  Month of Registration

SMITH, Lorenzo P H Wandsworth London 1995 July
SMITH, Lorenzo P H Oxfordshire Oxfordshire 2003 June
SMITH, Lorenzo    Wandsworth London 2003 February

The details of the first two are:

Name: SMITH, Lorenzo P H
Registration District: Wandsworth
County: London
Year of Registration: 1995
Month of Registration: July
Spouse's last name: Blount
District No: 256
Page No: 0003
Ent No: 016
Source Code: C12

Name: SMITH, Lorenzo P H
Registration District: Oxfordshire
County: Oxfordshire
Year of Registration: 2003
Month of Registration: June
Spouse's last name: Symons
District No: 695
Page No: 0711
Ent No: 167
Source Code: R10

I can only imagine that these are both for him and that the first marriage ended in divorce.
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If the first marriage is kosher, there are three possible childre with the mother’s maiden name of Blount:

Name  Registration District  County  Year of Registration  Month of  Registration

SMITH, Jack William Leicester Leicestershire 1995 January
SMITH, Joe Henry Leicester Leicestershire 1999 September
SMITH, Thomas James Leicester Leicestershire 1996 April
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And the second marriage would show:

Name  Registration District  County  Year of Registration  Month of  Registration

SMITH, Joey Ben R Southampton Hampshire 2006 February
SMITH, Leon Matthew Southampton Hampshire 2003 January
SMITH, Sadie May C Southampton Hampshire 2004 November
SMITH, Thomas Ronnie Hampshire North Hampshire  2005 December

To resolve this would require buying the marriage certificates to show the father’s full name, his age and the name of his father.
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