With 12Volt 13W LEDs, you'll draw I = Watts/Volts = 1.08 Amperes per lamp from the battery. One LED light switched on for 14 hours will consume 15 Ampere-Hours of the total number of amp-hours available from each battery. Multiply that by the number of LED's (25) to find the total capacity needed: 375 Amp-hours.
Perhaps the '550amp' you mention is actually 550 amp-hours, the battery's total storage capacity. If so, you're already set. If instead it's the 'cold start cranking current' that is sometimes used in battery specifications, you'd need to look around for what the storage capacity specification is. Make sure it is of the so-called 'Deep Cycle' variety, designed to provide a medium-sized current for a long time rather than a lot of current for a short time.
LeeH
p.s. You also asked about how many watts of solar generation capacity you'd need. Your 25 LEDs will use 325 W. It's unclear if you'll want them on all day or part of the day. Let's say you don't need them all the time and just need 200 W on the average. The battery storage-release is only around 90% efficient, or worse, so maybe you'll need around 250 W average power generation over the day. Since there's no sunshine at night and you will also want to handle some cloudy days, it would be a good idea to have about 1000W peak solar capacity. BTW, the need to handle cloudy days suggests that you might want some excess battery capacity too. Mike W.
(published on 08/22/2012)