The word "a lining" has got nothing to do with drawn lines (it's something about fur and fabrics apparently...). There is also no verb "to line" that means "the act of drawing a line".
But there does exist the verb "to underline" which means "the act of drawing a line under words in a text". What is the corresponding noun? Is "an underlining" correct? As in:
When I underline important words I make a nice underlining.