See th eDictionary of the Scots language at www.dsl.ac.uk, s.v. 'loan':
"Orig., before the enclosing of fields, a strip of grass of varying breadth running through the arable part of a farm and freq. linking it with the common grazing ground of the community, serving as a pasture, a driving road and a milking place for the cattle of the farm or village and as a common green". You will also find the compound 'loan-en(d)' there. They derive it from the same ancestor as standard English 'lane', though I wonder if some relative of the Gaelic 'lòn', a marsh, a meadow might be implicated too.