You didn't specify many details (like what kind of Energizer Lithium battery you are using), but...
lithium batteries tend to bounce back a LOT when removed from a circuit, so if you are turning the light off, unscrewing it, and pulling the battery out, then testing it, it may be reading 2.8V when in reality it may be running at 2.0V or less under load. If it's the CR123 battery, it could develop a 2ohm or higher resistance at that point, restricting it's current capabilities a lot. Those 2 in combination (low source voltage and high source impedance) will starve the converter board for power and hence lower the light output.
You didn't say how long this takes either.... my questions
What lithium battery (specifically) versus what alkaline batteries (specifically).
What is the runtime for each before they dim?
If the lithium is running 3 hours before getting dim at 2.8V float voltage, and that alkalines are running for 1 hour before dimming, then I'd say there isn't an issue here. Alkalines don't recover nearly as fast or far as lithiums, so if you measure a pair of alkalines at 2.8V, they really are at 2.8V (or close to it) depending on load, but they also sag a lot under high currents, so they have some life left in them probably but will begin dropping quickly at that point, but a 3.0V lithium at 2.8V "floating" is going past the "knee" in it's discharge curve towards imminent death.
If you use 2 AA Energizer E2 Lithiums compared to 2 AA Energizer alkalines, you should easily get 2-3 times the runtime before they run out, if that's not happening, then more information is needed. If you run 1 123 Energizer Lithium, your runtimes should be roughly equal probably.
Anyone knows what is going on?
