I've lined bags! For a felted bag:
1) finish your felted bag; make sure it is bone dry before proceeding
2) sew up your lining of choice, making it BIGGER than the dimensions of the felted bag
4) sew patch pockets to the right side of th e lining if desired
5) turn down the top edges of the lining and sew into place
6) turn the lining inside out, drop it into the well of your felted bag
7) take neat hand stitches through the top of the lining through all thickness of itself and the felted bag, about 1/4" down from the top edge
By making the lining BIGGER than the bag, you will never have any strain put on the lining, or the stitches that secure the lining to the felted bag. It's important to make the lining bigger.
I'm sure other KH-ers have other methods that work too!
But that is how I did it.
On my daughter's Booga Bag...I didn't line it...but I felted a large extra rectangle by itself, and handstitched it into place inside the Booga Bag!
It worked, too!