What current should I charge/discharge my 12V lead battery at?
You can charge and discharge the battery over a wide range of currents but the information on the side of the battery indicates values that the manufacturer accepts as reasonable.

You can charge it with a constant voltage supply of between 14.4 and 15.0V with limited current that will ensure the current into a discharged battery does not exceed 6A.

You should disconnect the battery when the current falls below about 1Amp (1/20C) which should occur in about 5-10 hours if fully discharged.

The other mode of charging is 'Standby Use' where a constant voltage is applied to the battery and it will charge itself as necessary - this mode of operation is often used for standby power supplies rather than cycling charging then discharging (called cycling).

It is not recommended to charge this with a constant current because the voltage can easily go over the 15V level at the end of charge and this will cause the electrolyte to gas and be lost - there is no provision for topping up the electrolyte on this type of battery

You can use a lab supply for this but I recommend that you put a diode in series to avoid the battery discharging back into the supply if the power supply is unplugged or switched off.

The information on the battery also indicates the acceptable discharge currents and capacity - at the 2 Hr rate the capacity is 16AH - this means that if you discharge it with 8 Amps it will discharge in 2 hours.  It will probably be acceptable to go up to ~2-3 times this value (i.e. 25 Amps) without damage although the battery will discharge more quickly.  If you discharge more slowly you will get more total energy out of the battery, at 1 Amp it will take 20 hours to discharge.

There is no lower limit to discharge the battery but at very low rates you may lose more energy to self-discharge than powering the load - the battery will discharge all by itself in a few months. 

I recommend that you learn about batteries from somewhere like Battery University.

Note - you will often see the 'C" terminology related to batteries - this is merely the capacity in Ampere-Hours (AH) expressed as a current, for example this battery has 20AH capacity.  If you discharge it at 1/20C (0.05C) this means discharging it at 1Amp.