If the battery is totally dead, a motorcycle with a carburetor might start if the kick starter is kicked fast enough and the headlight/parking lights are turned off.
Then again, it might not.
Kicking it over fast will cause the alternator to produce a little electricity and it may be enough to activate the ignition coil to produce a spark.
Having several people give the motorcycle a push while it is in 2nd or 3rd gear and then releasing the clutch to make the engine spin over is more likely to rotate the engine fast enough to produce the needed electricity.
A fuel injected motorcycle probably won't start using the same method because the fuel pump must run to build up fuel pressure and it is doubtful that a short push would be enough to do that.
All batteries produce less power when they are cold.
They rely on chemical processes to produce power and cold slows down these processes.
That said, a noticeable decline should not be seen until the temperature drops below 4.4 C.
Even new batteries can be defective. What is more likely is if the motorcycle is run at low speeds on a number of very short trips the alternator will not have time to recharge the battery. Each time the motorcycle is started a large amount of current is required and if it is not replaced the battery charge will get weaker and weaker.
Motorcycle batteries do NOT like Quick charges so taking it to someplace for a high power recharge may get the battery recharged but at the cost of destroying its life.
If the motorcycle is in neutral when it is started it should not lurch at all.
Once the engine is started it is quite common for it to lurch when you pull in the clutch and put the transmission into gear.
The reason for this is the clutch plates (there are several like layers in a sandwich) tend to stick together when the engine is not running. When the clutch lever is pulled in for the first time, two or more of the plates may stick together, transmitting some power into the transmission. When the gears engage, this power will try to drive the motorcycle forward.
As soon as this happens, the plates will loose their grip and start slipping like they are supposed to do and the motorcycle will stop moving. It will lurch while this is happening.
Something that will help to reduce this clutch sticking is to do the following:
1. With the engine not running, pull in the clutch lever.
2. Extend the kick starter lever.
3. Push the kick starter lever down. It will show resistance until the clutch plates break free and will then move down freely.
Once this is done, start the engine, pull in the clutch lever and put the transmission in gear. There may be a slight "clunk" sound as the gears engage but the motorcycle should not lurch noticeably.
Have fun riding your RE.