Hi Codam,
If you don't have a post-1855 death certificate then it will be almost impossible to prove who his parents were. Between 1816 and 1822 (according to the short-lived Dalziel Parish Bank) there were 3 distinct families of Lindsays in the parish. 1 each in Motherwell, Flemington and Windmillhill. (All Motherwell nowadays). In 1810 Lindsay of Netherjohnston paid rent to Dalzell estates for his farm. (That may have been the Flemington family). The same year another Lindsay paid five shillings feu duty to Dalzell estates. In the Dalzell rent collection of June 1812 John Ferguson paid 2 years rent from Martinmas 1811 for the house at Barrons.
There are 2 monumental inscriptions taken from the old Manse burial ground (until the late 18th century the parish church had been situated there).
"William Lindsay aged 73 years. Isabel Tugh his wife aged 64 years. John Lindsay aged 25 years 1818. William Lindsay junior died 13th December 1823 aged 39 years". On the other side of the stone - "Erected by James Lindsay in memory of his wife Margaret (Ferguson) ............................... the rest has eroded. (Ferguson = very worn).
(Pity there are no dates of death for William and Isabel).
2nd stone - "1852 John Lindsay died 1826. His son Robert died 28th April 1874 aged 73 years. (His wife Marion Brownlie died 16th June 1874 aged 74 years)".
In 1789 a new church for the parish of Dalziel was erected at Windmillhill. This is now known as South Dalziel, although it is no longer used as a church.
2 monumental inscription from that churchyard may interest you.
"Erected by Alexander Lindsay and Ann Wood in memory of their deceased children. The above Alexander Lindsay died July 1896 aged 65 years".
"John Lindsay died 23rd November 1890 aged 60 years. His wife Catherine Prentice died 30th May 1899 aged 69 years. His father died 9th February 1864 aged 59 years. His mother Catherine Brownlie died 4th January 1879 aged 77 years. His sister Elizabeth died 17th September 1864 aged 19 years".
Pity his father's name isn't mentioned.
Perhaps some of the names may have filtered down to give you some other clue.
Barons was not a village or even a hamlet, there would only have been one or two houses down there, very possibly connected to workers on the Dalzell estates. It was quite remote, although until 1789 it was handy for the church!
Good luck,
Lodger.