Power is power.
Power is Volts times Amps
Power in does not equal power out because of losses.
Too many people get hung up on "controllers," and with a modest system, such as is described in the initial post, one really is not needed at levels below 4 amps, and really of limited value at 5 Amps- as long as water levels are maintained. 45 Watts at 12 volts is not even 4 amps. It takes at least 13.8 volts applied to overcome internal resistance within the battery.
10 Amps at 12 volts is 120 Watts- You can do a lot of lighting with LEDs these days, especially with the newer "Power LED" options, and used without a focusing lens, will radiate close to 180 degree dispersion from the mounting plane.
If you take a shortcut and use the homecenter undercounter puck lights, measure your current draw, each puck light should be in the neighborhood of 60 milliamps. At 12 volts, it is less than 1 Watt. Lite On has a 1 WattPower LED comparable in light output to that of about a 20 Watt incandescent light bulb. At about 6 bucks a pop- easy.
The power LEDs are supposed to have a heatsink behind them for their own heat- but mounting them with a little heatsink compound on a metal surface is actually adequate for the 1 watt power LEDs as they do get warm, but not at all a fire hazard.
So- Step 1- Determine how much lighting you need. try www.digikey.com, and order a catalog- they ship worldwide. You can look at pages online too, and you can enter the manufacturers into the search box, Lamina, Lite On, Lumex, Avago, and there are a couple more too, plus you can edit the pageurl to move through the pages too.
Step 2- Determine your total load, and length of time of that load. to come up with your ampere hours. With LEDs and good lighting habits, a single Deep cycle may be adequate. Size your batteries accordingly. Well maintained batteries will last well beyond their designed life expectancy. So oversize your needs 50% to 100% for "busy days" or emergencies If not even slightly more. At most, you only want to draw down to 80% of battery charge capacity regularly.
Step 3- From the above numbers generated for your expected load, What are you going to need for recharge capacity on December 23- right around the shortest amount of daylight per year? Select 50% above this amount to compensate for circuit losses.
Oversimplified in many ways, yes. But it gets to the heart of what people so far have been trying to put into words.