Yes Lincolnshire is a county name, but in those days it was divided into three ridings (Lindsay, Kesteven and Holland)
'Parts' I think rather than ridings, which is what Yorkshire was divided into. So you got Parts of Lindsay, Parts of Kesteven etc..
I think between us we have explained the insignificance and origin of the common "Messrs." prefix in early 20th century Britain.
I'm sure there would have been an equivalent in the USofA at that time.
In business, when writing to another company (as opposed to an individual) the letter would always be addressed to (for example) "Messrs Smith & Jones Ltd", then starting the letter with "Dear Sirs,". It was, as already stated, a shortening of the French Messieurs but why a French word was used is lost in the mists of time.