Falkirk council has results by counting area (based on Scottish Parliament consituencies) with the same disclaimer about postal votes as the Lanarkshires.
Falkirk East: No 54.5%, Yes 45.4%
Falkirk West: No 52.3%, Yes 47.6%
(both add to 99.9%, so I think they're based on totals including rejected ballots)
OTOH Fife council's website says "Please note that on instruction from the Chief Counting Officer we only have one Fife total available, we don't have a breakdown of results by ward or constituency."
Coatbridge 0.527752422 Labour
...
Airdrie et al. 0.482329843 SNP
Ding Ding Ding
... and given the thing about postal votes being spread around and that part of Airdrie was included with Coatbridge, the actual difference between the two towns was probably bigger than that.