I have a simple circuit using a TL431 (or LM431). As shown, it was optimized for a 12V lead-acid battery, and trip point is adjustable from 10.7V to 11.6V. If you want a different trip point, the LED lights when the voltage on the REF input to the TL431 is less than 2.500V, so recalculate the voltage divider consisting of R8, R6 and the 1K trimpot (R3 & R4 in the simulation).
The Plot shows the total current drawn by the circuit as the input voltage sweeps from 10V to 12V for different positions of the Trimpot wiper (0<k<1000). Note that the current drawn by the circuit when the input voltage is above the trip point is less than 1mA. For the value of R5 shown, the LED current is about 6mA when the input voltage is less than the trip point. If you want more LED currrent or change the operating range, you might have to adjust R5