I have an old Ayup battery (2010), that i used on Sunday night, the light is a claimed 800 lumens. The light unit is only a year or so old. It seemed not as bright as i remember and a fair bit duller than a newer 700 lumen L&M light.
Would the light output drop with an old battery?
It depends on the quality of the battery and whether the light unit is digitally regulated or just take straight voltage from the battery.
I believe that the Ayup lights are quite simple and rely on a resistor rather than using any fancy electronics.
It shouldnt dim, most led's run at 2V or that sort of magnitude so unless* its lot of leds in series the voltage will be being dropped by the driver.
It wont be just a resistor dropping the voltage as that would be massively inefficient.
*Not uncommon, ive got one of those nitefighters with 7 led's which iirc are series.
LEDs are current regulated IIRC, so the voltage doesn't matter that much.
LEDs generally have a current regulating driver, which is why they don't get dimmer as the battery drains in normal use. An old battery should charge to the same voltage as a new one (about 4.2V per cell), but the voltage will drop more quickly with use.
LEDs do age and reduce output with use.
Aside from the fact that claimed lumens are frequently entirely fictitious, comparing lights on lumens can be very misleading. A relatively small difference in beam spread leads to a big difference in light intensity (the amount of light hitting a given area) which is what you perceive.