You'll also need heavier thread. I usually opt for a polyester or nylon, even tho most everything you read says use cotton on leather. I've repaired many a leather biker jacket, sewn on many patches, repaired motorcycle seats, chaps, etc. Most are in all kinds of weather & frankly cotton thread just rots. In a pinch carpet thread can be used. Cordona thread is heavy, but it make be too thick to pass thru the eye of a leather needle. They make a special needle for it.
A leather needle has a wedge shaped tip that "cuts" a hole in the leather to allow the thread to pass thru. Unlike fabric, which is woven, leather is a solid. So once a hole is punched in it, it's there for life. So with each pass of the needle there is a hole. It's best to sew over the beginning & ending & not do any back tacking. Pull threads to back & hand tie off.
I'd also suggest using a tear-away stabilizer on the underside. It will help prevent the lining from getting torn by the feed dogs. If you don't have any just use a piece of computer printer paper. Heck I've even used newspaper in a pinch.
Because leather can stretch & is never completely dry it often sticks to the pressure foot. A leather roller foot helps, but if you dont have one I suggest using a jeans foot.
It's not as hard as it sounds. You just need to take measures to prevent problems.