While other good answers have stated why discharging a 12V lead acid battery is hurtful to it, I seem to be unable to find how you should monitor it.
Assuming I want to stop drawing current from the battery when it is at 50% charge, to avoid too much permanent damage. When the answers like this one states the amount of cycles you can have with each DOD, it does not state how it should be measured. As voltage drops during discharge, the battery may (correctly) show a lower voltage with a multimeter than without any load on it, where it will quickly rise to a larger voltage.
To avoid damage, should I stop drawing current when the battery is at 50% during a discharge, or when it is at 50% with no load?