Recharge household batteries?

Your pictured AAA Energizer Ultimate Lithium claims a shelf life up to 20 years, which works out to a self discharge rate of under 0.4%/month.

 

Mine didn't last 20 years
It didn't last 20 MONTHS - but it wasn't in storage.

The Romeo 7 doesn't have shake-awake but at my settings the AAA has a 50k hour energy budget (5.7 years.)
FORTUNATELY I have a calendar reminder to replace the cell at 36 months and I had the "installed" date on the sight.
I also have the ability to swap put the battery twice (depending on ROI for a lithium replacement versus an alkaline) without re-zeroing the optic.

Again.
Sample size = 1.

 

Many of today's devices are never really Off, just sleeping. Their sleep currents vary enormously.

Those Energizer Lithiums don't contain any more mAhs than their alkaline stablemates, but do maintain a significantly higher output voltage over their operating life. I can easily imagine cases where that higher voltage produces a considerably higher current draw (more than would happen with constant-R), greatly reducing battery operating hours. And a few items are simply incompatible with these lithium voltages. Merely inserting the batteries destroyed one device I had. No smoke, it just quit working, permanently.

Without detailed knowledge of the internals, it can be difficult to predict the results.

 

Concur.
I reread the manual Romeo 7s) that came with the sight and discovered that the sight DOES use a 'shake awake' to achieve the 50,000 hour rating, but as you pointed out very few electronic devices are ever truly asleep and it takes very little motion to wake up a gun sight.
The Lithium was the OEM battery and Sig put it in the sight for a reason - maybe because it's a green LED instead of a red one.
Like Kermit says.....It's not easy being green.
Lower wavelength.
More energy for the same light in the LED.

The OEM light lasted < 24 months, real world.
My intentions are to replace it with a like unit and check for function more regularly.
Everybody recycles batteries these days (or they SHOULD!)

 

That would certainly be a prima facie indicator that this device is compatible with lithiums. Lithium disulfides, that is, not lithium-ion.

 

Yep.
A bit off the OP - buuuuut that's PC