The solar part really depends how critical the application is.
Like, how many days in December are you willing for the lights to not stay lit all the way until dawn?
Also it depends on the location, azimuth, angle, shading, and soiling of the solar panel.
You are saying you need ~240 watt hours per day, i.e 7.44 kWh for 31 days in December. I would use
PV Watts to find the solar panel size to get that bare minimum as an average for December. For perspective, in my area with ideal exposure that would be about a 100W panel. But I would then multiply both panels and battery capacity by some factors to account for how reliable you want this thing to be. Say, double the panels and do enough battery for 5 days (accounting for acceptable depth-of-discharge as ggunn is pointing out), if that's what you need. There will be days without enough sun.
A single 12V 18Ah battery is nominally only 214 watt hours so that definitely isn't enough for your application even if it's a chemistry with a better depth-of-discharge than lead acid. Then if you want multi-day reliability you should be multiplying your battery capacity as mentioned above.
Also regardless of battery chemistry, if you don't want to damage the batteries you need some kind of electronics to shut the load off when battery charge drops too low. Hence using an off-the shelf solution might be better.