I line all my felts and furs. There are many ways to line hats. I generally cut fabric to fit the shape of the hat. The lining is attached to the hat under the sweatband with even stitches, for a neat presentation.
There are a couple of ways to help the crown tipper to stay in place which usually makes everything stay in place. One is an old milliners trick and that is to back the tip with light crinoline (not crin but the fabric) and it will stiffen it to the point where it holds it up. The other is to cover the tip with a clear plastic (usually with your logo underneath) and it serves the same purpose. I use that in all my cowboy and fedora hats as well as my Derby hats. Here it is on one of my bowlers but it works the same way and everything stays in place nicely.