Linage means payment for written work at a specified amount per line:”I have agreed to translate a book on the condition that I should be paid on the basis of linage, not on the basis of chapters or total number of pages.”
Lineage , on the other hand, means the descendants of a common ancestor considered to be the founder of the line of ancestors:”She, being a cousin of the royal lineage, doesn’t like to mix with common people which may cause her defeat in the elections.”