Suppose the minimum forward voltage of a LED is 3V and the capacity of the battery is currently at 3V as well.
Can a LED draw beyond it's minimum forward voltage?
I believe the answer for the Fraz circuit is No.
I believe the LED would turn off when the battery goes below 3V.
looking at the excellent data you collected in
this post, the only LED with a forward voltage lower than 2.5V is the Red SST-20. For the LH351d your list shows a minimum forward voltage of 2.7V.
My guess is that the Fraz can not draw a battery below 2.7V, when using the LH351d.
I like where this is going. Thanks to your data collection and questions, it appears the Fraz with an LH351d would be unable to overdischarge a LiIon, so it does not actually need to rely on a Protected battery, to prevent overdischarge.
The only LED on your list that poses a risk of possible overdischarge is the Red SST-20, whose minimum forward voltage is 1.8V.
Thanks for sharing your inquiries. Im learning a lot, with you, about the Fraz (I dont have my own).
disclaim: I have not tested to confirm these assumptions about the discharge limit imposed by the forward voltage of the LED in a Fraz. Im not an expert, seek confirmation.
trust but verify ;-)