I don't have a sewing machine either, but I like to line my felted bags. This link
helped me learn how to line the bag. While it didn't look perfect it looks great. I just found some cute cotton fabric that matched the colors in my purse, sewed the sides, the bottom corners and a ridge around the top and then sewed it into the top of the bag (but I didn't sew all the way through. It did take a long time, but that was my first one. Here's a picture. You can see where it is sewed in, but I liked the final look and the recipent loved it and that is what matters!
If you have any questions let me know!
Best of Luck!