This topic comes up often.
Can I run a lithium battery on my vintage motorcycle? Lithium battery in this article refers to: Lithium Iron Phosphate (LiFePO4) type.
Short Answer: No, we don’t advise this.
Here is why:
Lithium batteries are sensitive to the voltage at which they are charged. The stock charging system (zener diode) and solid state regulators rated max output tends to exceed the maximum charge voltage for this type of battery.
Lithium batteries don’t like to be charged at any voltage higher than 14 volts. This becomes problematic because the stock zener diode ZD715 is rated at 15 volts and capable of a bit more depending on heat sink size and thermal conditions. During testing on a machine we got results of 14.5-15.7 volts. Zener diodes convert excess electricity to heat and their performance my suffer in hot weather conditions. Or if the connection to the heat sink is corroded.
Solid state regulators, designed for lead acid batteries, charge at 14.5-14.8 volts. This is still higher than lithium battery specs recommend.
There are special regulators that are designed for use with  lithium batteries:
Rick’s Motorsports Electric – Hot Shot Regulator/Rectifier For Lithium Batteries – Regulates voltage at 14 vdc +/- .2 volts
Trispark also makes mention of lithium batteries it in a tech article: Click Here
While there are folks on the forums that have run lithium batteries on there stock bike. They have gotten lucky and not had a fire. I saw a picture of a lithium battery on a Norton Commando that blew up while on a ride. I wish I could find it again to share. It was not pretty and could have resulted in a fire that consumed the entire bike.
Of all the new technology available lithium motorsports batteries probably have the highest risk to benefit ratio. The most attractive feature is energy density. You can have a battery of the same dimensions that stores much more energy. For an electric start bike this may be advantageous. Besides this there is not much benefit. Weight savings is minimal. Battery lifespan is longer but product cost is higher. Cold weather is not kind to this technology.

 

Lithium battery in this article refers to: Lithium Iron Phosphate (LiFePO4)

These are not the same as what is in your: cellphone, laptop computer, electric bicycle, or Tesla car. These are Lithium-Ion and are a different chemistry and even more sensitive in nature. All lithium batteries can experience thermal runaway. This is a dangerous uncontrolled rise in temperature. The end result is often fire or explosion. Google lithium battery fire for more info.