If you are considering only LED lighting and no other use, allowing for the Arduino aspect, your concept may work well enough.
The primary reason for higher voltages is to reduce current losses through wiring resistance. Transmission lines are extremely high voltage for that reason.
In a configuration such as you suggest, the low voltage will have greater power loss due to wiring resistance, but it will be greater only by comparison to more extreme situations. Your wiring runs are likely to be short enough as to permit heavier gauge wiring to ameliorate resistance losses, without an excessive expense.
You will want to incorporate some fusing or breaker device for overload protection, as a 30 ampere-hour battery can provide enough energy to melt the insulation and/or cause a fire if inadvertently shorted.
You didn't mention a charge controller, nor the battery chemistry. You will want to ensure that you do not overcharge the battery and also to follow the correct charge profile based on the battery chemistry.
Lead-acid batteries, especially valve-regulated sealed lead-acid batteries do not do well with overcharging. Flooded lead-acid batteries will release acid vapor and damage surroundings when charged at high levels.
Lithium based batteries also have special considerations, outside the scope of this forum.
On the upside, free electricity is great, if you are able to balance your expense with the local utility costs.