Ive been using 48v power on my golden 36v controller and 36v hub for over a year now. Top speed is about 39 kph 11kph more than 36v and torque has improved slightly. I get more distance per ah on the higher volts as I move faster over the same time.
You are at risk burning your power resistor out using a 48v battery on a 36v controller.
Depending on your controller you may have to mod it or get a new one.
Because I use 24ah SLA's I don't care about LVC and with the mod I use its almost disabled. I don't even get close to 50% dod.
If youre are interested here I am looking at a new chip called the LM2576hv for mods and power regulators in controllers and bike lights that can tap right off a 60v supply and drop the voltage to a number of adjustable voltages. This chip is small, easy to use and is not like the linear regulators in most controllers found today. It uses a buck down step regulation over a inductor using pulse width fixed cycle rate at 52khz.
If you like tinkering and risking buying a new controller you have nothing to lose trying a mod. The worst thing could happen is you blow your controller and have to get a 48v one anyway.
The thing you may need to consider is if you have Lifepo4, that it does have an LVC
BMS and what type of controller you already have.