Electronic – Lead-Acid battery discharged to 5V – how much damage

Fortunately, there is. You can find diagrams of the discharging process of a battery type, search for "lead-acid discharge graph" or so. This returns graphs like this one:

In the datasheet of your battery you can find the exact graph for your battery.

Say you want a circuit to detect 80% discharged, just check in the graph, the voltage of a lead acid battery with 80% discharged is about 1.9V.

You can check this voltage with a multimeter, or use a comparator circuit or a microcontroller with ADC to make a dedicated device for this.

Your point can be very easily made differently.

If you look at the discharge curve for a Lead-Acid Battery with a 12V or 6V rating:

This comes from Yuasa. They make the things. It's either reliable or optimistic, certainly not pessimistic.

Let's look at the 12V one and optimistically assume that you are only interested in 0.2C discharge, any other rate the same arguments can be made with a different line.

At its 12V mark, you can see there is a "tipping point" where the voltage goes from relatively constant to plummeting.

At 11V it is almost going straight down.

At 9V it will drop right away under the same loading current.

This means that at the 12V point you have essentially used 60% of its capacity. At 11V you are at effectively 93%. At 9V you're at 99.5%.

Now adding that a battery with 0V across it has no chemical initiative any more, of any chemistry type, you will need to motivate it re-create the chemical imbalance that causes the apparent voltage and potential for current to flow. This is hard in any battery (which is why almost all batteries are built with electrodes already chemically built of the right materials to create the cell potential).

With SLA a lot of energy goes in chemical recombination of Sulphates and Sulphites, wasting a lot of energy. This results in needing excessive power to re-engage a cell that is left at 0V. Excessive power = heat. Heat = gassing. Gassing = moisture loss. Moisture loss = bad. Not to mention the higher voltage usually required makes many, many by-products on the plates, next to by-products already generated by neutering it in the first place and you're left with a AA battery with the weight and size of a 6Ah SLA.

Now, if you go near 9V, it will become 0V very quickly. You'll easily be too late.

Many manufacturers tell us "Consider your battery empty at 11.8V", some people (me included) assume 11V. Those who use 11V often (but not always) take care to know that this is the lower limit. This is exactly for that reason.

If they will not accept that 100's of manufacturers, countless experts in the field and users alike say "at 11.8V you're not going to get much more out of it and it'll be risky to try", then just convince them with the fact that at 11V there won't be much to get any more anyway. Done. All other points moot.

The reason a car battery can be dropped to 2V and then keep working, is because that battery was at 2V very shortly, because the idiot leaving his lights on realised after a while. And because they are usually over dimensioned by a factor of 2 to 5, depending on the type and brand of a car, so a crippled one will work for a couple more years.

And let's be honest, are we really going to put hours and hours of work and research into convincing someone who can't even manage to mind his car lights of agreed fact shared between thousands of electrical engineers worldwide?