I can't find a birth registered for Thomas Alexander LE BOT/LA BOT or any combination of name born 1903/4. However, looking at the Liverpool Catholic baptisms, there are only 3 children born with mother Sarah Gaffney:

Alexander LEBOT born 21 Oct 1898
Joseph LEBOT born 10 April 1901
Thomas James DUFFY born 4 Dec 1903
The latter was baptised 14 Dec 1903 at St Francis Xavier, parents Thomas James and Sarah DUFFY (maiden name GAFFNEY), godparents Peter and Christine HOLLAND.

Perhaps only a coincidence that this is the same date of birth as on the death certificate for Thomas Alexander LE BOT?

Joseph Alexander LE BOT had a child by his first wife, indexed in the baptism record as LAYBUTT:
St Augustine, RC, Liverpool
Born 6 June 1883, baptised 12 June 1883, Maria LE BAT, dau of Joseph Alexander and Catharine LE BAT (maiden name RILEY)
Godmother Maria FARLEY

Catherine LEBUT died Sep 1893 age 32 Liverpool.