Lead acid batteries should never stay discharged for a long time, ideally not longer than a day. It's best to immediately charge a lead acid battery after a (partial) discharge to keep them from quickly deteriorating.
A lead acid battery left in storage at moderate temperatures has an estimated self-discharge rate of 5% per month. This rate increases as temperatures rise and as the risk of sulfation goes up. Sulfating: This is a buildup of lead sulfate crystals and it occurs when a lead acid battery is left sitting without a full charge.
Ideally you can configure the cut-off coltage, such as with the depicted unit. So many lead acid batteries are 'murdered' because they are left connected (accidentally) to a power 'drain'. No matter the size, lead acid batteries are relatively slow to charge. It may take around 8 - 12 hours to fully charge a battery from fully depleted.
If at all possible, operate at moderate temperature and avoid deep discharges; charge as often as you can (See BU-403: Charging Lead Acid) The primary reason for the relatively short cycle life of a lead acid battery is depletion of the active material.
Since that is no longer an issue (and never was an issue with lead acid batteries) there is not a need to fully discharge. By discharging a lead acid battery to below the manufacturer’s stated end of life discharge voltage you are allowing the polarity of some of the weaker cells to become reversed.
Personally, I always make sure that anything connected to a lead acid battery is properly fused. The common rule of thumb is that a lead acid battery should not be discharged below 50% of capacity, or ideally not beyond 70% of capacity. This is because lead acid batteries age / wear out faster if you deep discharge them.