What are a 'coach lines'
Coach lines (stripes) are a type of thin stripes you saw on (typically British) cars. They were a hallmark on high end cars like Rolls Royces.  

See this image from from this article:



The coach lines are the lines under the guy's hand.

See also the wikipedia article on Pinstripes. 

My guess is that this bike may have had some sort of pin striping.