You could patch it - if you can hem, you can do this though it takes a bit of patience.
Buy a small piece of material of similar weight and shade to the lining, along with suitable thread - a specialist sewing shop should be able to advise you if you are unsure.
Cut a suitable shape to cover the tear, turn over the edges, and iron them flat.
Unpick a length where the lining is sewn to the coat, so that you can get your hand inside.
First pin the patch over the tear, then tack it (long loose stiches to hold it in place) - make sure it lies flat, and completely covers the tear. Remove the pins.
Then stitch securely in place.
Finally, remove the tacking, and resew the lining to the coat.
Rosemary, May 2009