This feels like quite an obscure one, but I’ve been asked, so I’ll answer!
Your lineage is your ancestry or pedigree.
Linage is the number of written or printed lines.
In the spirit of trying to write at least one example that uses both of the words discussed in the post: “How much linage do you need to write out the Earl’s lineage?”
For more troublesome pairs, look at the category cloud to the right, or click here.