One of the listings in the 'Community Contributed' International Genealogical Index for the baptism of Janet Thomson in 1777 says that she was born at Easter Glentore, New Monkland. Normally I would not trust as far as I could throw an overweight lead hammer anything in the 'Community Contributed' IGI.
If, however, after looking up the original of the baptism on Scotland's People, it turns out that Janet's parents were 'of' Easter Glentore in 1777, there is a listing in the Index to the Register of Sasines for Lanarkshire that may be of interest.
Thomson, Andrew, portioner of Easter Glentore, wright, Airdrie, XVIII.140; XXI. 42, 181
Thomson, Andrew, portioner of Easter Glentore, son of James T, portioner there, XIV. 4, 121, 333
Thomson, James, portioner of Easterglentore, XIII.426
Thomson, James, portioner of Easterglentore, son of Andrew Thomson, portioner there, XIV.333; XVI, 367; XVIII.140; XX.482
Vol XIII is from 1721 to 1729. Vol XIV 1729-1745. XVI, 1751-1760. XVIII, 1766-1769.
Then in the earlier book
Thomson, James, portioner of Easter Glentore, son of James T there and of Bogsyde, IX.384; XI. 475; XII. 369 (bis); XIII.36: his spouse, see Margaret Dick
Dick, Margaret, daughter of John D in Midlequarter, and spouse of James Thomson, son of James T in Bogsyd IX.384.
Vol IX, 1688-1693; XI, 1699-1709. XII, 1709-1719. XIII, 1719-1720.
James Thomson and Margaret Dick had at least three sons baptised in New Monkland: John 1694; Andrew 1696 and Matthew 1698. There's also a Thomas baptised in Leith in 1704 either to the same parents or to a couple with the same names.
There are almost certainly later sasines referring to Andrew Thomson of Easter Glentore, but the printed index books only go to 1780. After that you have to access the information in the Historical Search Room in Edinburgh.
I cannot stress enough that before you attempt to tackle the sasines, you must check all the baptisms to see where the parents' residence was.