From you attachments, the batteries seem to be a regulated (to 1.5v dc) lithium ion batteries. AAA batteries of this type have safety things in them for over current and such. If you flashlight draws more than the over current safety on the the battery it will shut down. For this type of battery about 1.5 amps is over current. I believe from your attachments that there are 3 batteries (Just guessing) are in series, making 4.5v dc. That would seem correct for lighting an LED. I'm going to guess that you flashlight is pulling to much current out of the AAA batteries.
Now, the lithium 1.7v dc batteries that you refer to are known as Lithium Iron Sulfide (ie, Energizer type). They are relatively safe and come without any protection circuits. But they too have an over current of about 1.5 amps. They won't go into shutdown, all these do is drop their voltage due to their internal resistance.
I do have a hard time believing that this flashlight will draw all that much current from AAA batteries. Maybe try this flashlight with alkalines to see if they work at all. Alkalines should be ok too, but will not last long if this flashlight draws a lot of current. If you put in a set of fresh alkalines and it doesn't light, then there is a very high current draw. The next step is to try the Energizer type lithiums. These are pretty expensive today after covid for some reason. (Maybe supply chain stuff).
If there is another regulator inside the flashlight (or a driver circuit), that may have developed a problem. Of simply, you may have the strobe turned on....maybe a reset to that driver circuit needs to be done. Try tapping the button multiple times to clear out of the strobe.
I know, I'm long winded. Sorry about that.
