Flow Batteries[1]!
They work (as in: are being used in Africa & South America to power mobile networks). Also my (office) building is powered by one.
They don't cost much more than lead-acid
They last much, much longer than lead-acid or lithium*
There is no limit to the number of power cycles(!!) and they can be deep-discharged.
They do have disadvantages - they aren't suitable for cars, and are currently fairly noisy when cycling, and have lower power density than lithium* batteries. They also need to be periodically complete discharged (although most have software to make sure each individual cell does this as part of the normal use)
Disclaimer: An investor in Redflow owns my building (hence the power source)[2]