I'll try to answer your question.
Your lead acid battery has a capacity of 23 Amp hour. If you discharge the battery at a current of 1 amp, it will discharge in 23 hours, theoretically. The actual capacity depends on how quickly you discharge it. Discharging it in say 1 hour (at 23 amps) it will not give 23 amp hour. The other problem with lead acid batteries is that as they are charged and discharged, their capacity is reduced.
Attached is a chart from an aussie battery maker. If you discharge your battery at a rate of one twentieth of the one hour rate (23 x 0.05 = 1.15 Amp), then according to the chart, the battery will maintain its terminal voltage for about 2 hours. If the discharge is kept to less than 15% of capacity, the battery should suffer no drop in capacity for at least 1600 cycles. (thats about 5 years.) After about 2500 cycles, the battery capacity could be reduced to 60 % of its capacity or about 14 AH. Thats after about 7 years.
Hope this helps.
In your case with 3 LED discharging at 0.5 amps, if you operate the leds for 4 hours per day, the discharge is 2 AH. ie 2/23 = 8.6 % per day. This is a very light loading and you should be able to run 5 lamps at 4 hours per day to give a 14.3 % discharge per day.