I have my filtration and heater connected to a computer battery backup. I do not have the lights connected as they are not necessary. Actually the lights are connected to an outlet that is controlled by a wall switch.
Aquatic stuff does not take a lot of power. The largest draw for me is the 100 watt heater. I figure that the battery backup should keep the filtration and heat going for over a day.
This is similar to what I have:
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This does not help in your current situation but may be a thought for the future...