This 12V LiFePo4 should be good enough for you. 0.48A for 12hr is 6Ah, so 16Ah will be plenty for you. And preventing full discharge you typically add 20% capacity so that % doesn't get used for the health of the battery.

Also the solar panel might be fine, but you need a CC-CV controller to properly charge a LiFePo4 battery. It should charge up to 14.4v max, 14V to cut off the top .1v.

What you could do is use a CC-CV DC-DC from the MPPT controller (needed to ensure solar panel efficiency) to charge the LFP battery. Then have a small relay that is powered open by the solar panel MPPT as well, so that when the solar panel can't produce any more power the battery begins to power the LEDs. 20W would be more than enough to power the system. You'd likely have excess power.

If that's a picture of the power pack that's in the fixture it tells what Voltage the LEDs in your fixture need. If it's 12 volts just bypass it directly. If not, replace it with something like this:
https://www.amazon.com/DZS-Elec-Converter-Adjustable-Regulator/dp/B07L9V4S39/