I've heard the term cathode ray pretty much every year in school since they introduced chemistry, and I know that it's a stream(?) of electrons. I'm just having troubles relating it to the real world. I think lightning would be a prime example, but I'm not sure; looking for confirmation.
As you are already aware, cathode rays are electron beams. You take evacuated glass tube, and add two electrodes on either end. Once you apply a sufficiently high voltage, a stream of electrons flows towards the "cathode"; this is what you call a cathode ray. Inside the tube there exists near perfect vacuum, so there are barely any other gas molecules, ions etc.
Lightning is similar in the sense that you have a large potential difference that leads to electric discharge. The key difference is that this takes place in air, and not in vacuum. Since air is "insulating", it has to be ionised to for the electric discharge to take place. Indeed this is what happens, when the potential difference is sufficiently high. However, what this creates is a plasma, not a stream of electrons.
A plasma is the "fourth" of matter, and is created by ripping apart some electrons from gas molecules resulting in a collection of electrons and ions.