In reading I find a flooded lead acid battery should not be discharged below 20%, and, preferably not below 50%.
There are very few and specific applications that may be true. A standby battery used for a ham radio station isn't one of them. Probably your greatest limitation of operating voltage isn't the battery, but the equipment you may be running from it. Often, transceivers are rated for 13.8VDC, +/- 15%. That puts the lower limit of voltage to be around 11.73V, which depending on the battery and other loads is only about the 50% point. So review what the operating voltage range is for your equipment and what the net run time you'd get would be directly connected. If that's not enough you'll either have to use a greater Ah battery/battery bank or a battery booster that will allow you to realize all the Ah your battery has.
The option I use is an AC inverter, and operating the equipment off of 120V. Many will exclaim the inefficiency of this but the overall net I get by using all of the battery's capacity instead of just half, it works for me. Connections, charging and switchover are other benefits to using an integrated inverter unit. A computer UPS can often check all the boxes for this.
Is there a device that will discontinue the load when a preset discharge level is reached?
Sure, do a search for battery low voltage disconnect. I don't think you need one at all. I don't want something cutting me off when operating in an "emergency", the communications is more important than the battery. Plus, most equipment is going to crap out before the battery is totally dead anyway, so it's a self solving problem. Instead of a disconnect, get an inexpensive battery monitor that allows you to see voltage, current and Ah at a glance which tells you all the important things you need to know while you're using the system.
Discharge level is referenced to the voltage under a mild load. A 100% wet cell charge level would be around 13.3 volts. The 40% charge level voltage would be some whare around 12.4 volts.
None of that is true for lead acid. State of charge can be determined at any discharge rate including static/no load and the voltage representing state of charge is highly dependent on the battery, battery merit and operating environment. Read that to mean using terminal voltage alone is a highly arbitrary means of determining SOC.
As a rule of thumb do not discharge the 12 volt wet cell battery below 12.5 VDC (50%) if you want to have a usable battery for many years.
Lead acid batteries have a finite calendar life, no matter how little they're used or how well they're maintained. Any deep cycle battery is capable of many hundreds of cycles down to 20% SOC. At a practical level, for ham radio uses you could run a battery down once a week,
for years, and never wear it out before the battery expires from age.
Mark K5LXP
Albuquerque, NM