I had a look at the 1901 census for Herbert Dexter born 1889 +/- 20 years! There are only 15 of them. Obviously some are too young to have an occupation, so I looked at their father's occupations and none bore any resemblance to lace working. Not that this means anything, but it's all I could think to do with nothing else to go on.

Anyhow the only one remotely connected to anything like lace making was the one Carol already found and I suspect it's the same one in the 1911 that Bilge found. By the way Bilge - was that 1911 Herbert Dexter married?.
Here he is anyway:
1901
23 Stratton(?) St
Nottingham
RG13/3173/187/29
(all born Nottingham)
Sarah Y or J Dexter head wid 58
Thomas son single 32 hosiery warehouseman
William H son single 28 do
Herbert son s 25 lace do (so lace warehouseman? not exactly a maker

)
Annie E daur 19 hosiery machinist
Ada daur15 shirt maker
Herbert son single 25 lace
We really need to get an idea of the year of birth of Peter's Herbert Dexter.