Bernard - I have done a little research on the Lestourgeon family.
There were at least 4 Davids, of which the first three were watch makers. I & II are as identified in Loomes (Allan #14) The David born in 1665 is the one that was admitted as a Brother possibly in 1797 rather than 1798 as normally quoted. I believe he was the maker of your watch.
He was married to Maria Anne (Marianne) and although Loomes identifies a ceremony on 1 April, 1701, there are records of the baptism of Maria Anne on 12 March, 1693 as well as Elizabeth 21 December, 1701. Although I cannot find a record of the birth of David III, he was apprenticed to his father 3 April, 1704. So on the basis that this is unlikely to have commenced before he was 14, he must have been born <= 1690. David II's death is well documented, together with his will in 1736. He is recorded as watch maker and inn holder In Finch Lane from at least 1707.
The apprentice records show that David III remained under his father until 5 June, 1721. I infer that it is at sometime in this period that he started to contribute significantly to the Lestourgeon output. He is recorded as CC from 1721-51.
David Thompson in Watches describes a watch now in the British Museum which is dated as 1702 from the inscription and carries a production number of #5448 ..
These photographs and the description from the BM ...
"Lost last Saturday night, the 16th instant, in or near St. James's Park, a silver pendulum watch, the maker David Lestourgeon, with a silver chain, the pendulum upon the dial plate, with the Queen's-Head upon the inside plate, and underneath Reg. Incipit. 8 die Martii 1702.
Whoever brings it to Mr. Lestourgeon, watchmaker in Lothbury, shall have one guinea reward, without being askt any questions."
London Daily Courant, 19 July 1709
(from research by W.R. and V.B. McLeod and John R. Millburn)
This watch is signed 'David Lestourgeon London' in two cartouches on the movement's back plate and in the middle of the back is the inscription 'Regn incip 8 mart 1702' beneath a portrait bust of Queen Anne with the insignia of state: orb, sceptre, sword and crown. This inscription shows that, although similar, this is not the watch that was lost near St James's Park. It is, however, a 'pendulum watch' and, like the Fardoil watch (registration no. 1958,1201.2347), it has a visible balance seen through an aperture in the dial.
....
David Lestourgeon, a Huguenot watchmaker, was married in Rouen in 1660. He went in 1681 to London, where he was naturalized the following year. It was probably his son, also David, who made this watch. He became a Free Brother in the Clockmakers' Company in 1698, perhaps having learned his skills from his father. His business was in Lothbury in the City, and he is thought to have died in 1731. ... The number 5448, punched into both cases, is Lestourgeon's production number.
If it was the David who died in 1731 (will 1736?) that was married in Rouen in 1660 he would have have to been in his 80s or 90s at his death. In the C18th this seems unlikely. I believe it is more likely that David II born in 1665 who came to London and made this watch (#5488) - the same David who made Bernard's watch (#2322) which I now believe was made very shortly after he arrived in London.
Given the apprentice records it cannot be the son of the David who was admitted as a brother in 1697/98 who made the watch, but it was the son of David I who was married in 1660 as Thompson indicates.
John
EDIT - I did consider that these two watches carry production (serial) numbers that are part of a sequence that was started in France and that the 'later' lower sequence of numbers were initiated in London possibly when David III started to become influential ~1710
