The lead piping going on the toilet ring is too short and do not cover the brass ring at all. I purchased a new lead piping section which needs to be solder on the old lead piping. How do I solder this lead section to the old lead piping?

Your best bet would be to replace the lead piping with PVC but that wasn't the question you asked was it?
You don't "solder" a lead to lead joint, you wipe a lead joint. A practice most of us older plumbers had to learn to get a journeymans license. I don't know about now but since lead is no longer used I believe it's a dying art. Call around to plumbing shops and ask if they have a man who can "wipe a lead joint" This isn't a task for the average home owner. Good luck, Tom

Speedball is experienced at lead pipe. I would stand behind his answer. If you are not experienced at wipe joints you need to avoid trying it.
Where did you get 4" lead pipe?