A lead-acid battery powering a Joule-Thief??
Rechargeable lithium batteries also do not like being discharged too low.
But the rechargeable Ni-Cad cell in each of my solar garden lights gets almost completely discharged every night for years without any problem.
The voltage stepup circuit is similar to the Joule Thief and a few of them do have the Joule-Thief circuit.
As long as we are on the subject - you can get a 1.5V to 5V step-up switching regulator out of an "emergency cell phone charger" that runs on a penlight battery. Quite small, reasonably cheap, and surprisingly well-regulated across a range of loads.
I only made mine to finish off all the AA's I got floating around. Yeah, Lithium's go into a 'coma' if they're discharge too low, parts of the chemistry undergo a chemical change that renders the bulk of it inert.
It's recharging severely discharged lithiums that causes problem. Electrolysis occurs causing highly flammable lithium metal to from from the salt.
This is why most battery chargers refuse to charge flat lithums and some batteries even have a protection circuit which disconnects the cell if it becomes too discharged.
I think the ferrite transformer I used was surplus from a MOSFET gate current drive setup. I think it has about a 100:1 turns ratio. Located what looked like the heaviest winding and used that for the base drive, and the other one for the collector winding. Used a BC639 first, then changed it to a BD139.
Both worked fine, with the BC639 getting about 0.5V min, and 0.6V for the BD139. Just goes to show, any old crap will work in this setup. Just vary the base resistor for the brightness range you want.
These devices cost $30.00 in the local shops in Australia:
As long as we are on the subject - you can get a 1.5V to 5V step-up switching regulator out of an "emergency cell phone charger" that runs on a penlight battery. Quite small, reasonably cheap, and surprisingly well-regulated across a range of loads.