All household electronics are made to be used in many different power quality settings.
If your 12 volt adapter puts out 12 volts when your power is 120 volts during the day then it will only put out 11 volts when your power is 110 volts or less in the evening. Rural power (at least in Canada) is often well over 120 volts hovering around 130 volts. So a transformer there would put out 13 volts.
So there shouldn't be too much risk in going a volt or two over. (Of course i don't know the tolerances for this specific LCD so be vigilant.)
You will want to use a multimeter in series with the DC side (not the wall side!) of the 12 volt transformer and find out what how many mA (millamps) it pulls.
Most batteries are rated for 1800 mAh (mA hours).
So hypothetically if your LCD draws 500 mA, then 8 batteries in series would run for about 3 hours.
However the voltage also drops exponentially over time with use. So you could maybe expect to gain 2 hours time from the LCD.
There for if you were to connect 16 batteries. Parallel in pairs, and then put the pairs in series, hypothetically you could get 4 hours of LCD.
I would recommend using a car battery personally Then you would get 100,000 milliamp. And you don't have to put anything in series. And it would last for about... *math in head* 53 years.
I would recommend going to a hobby store and asking someone there about batteries used in model planes. Usually those batteries are rechargeable, and come in 1.5, 6, and 12 volt configurations. And have a special charger to go with them.
Of course this is all hypothetical and someone more experienced in battery literature (i'm a commercial electrician) might know more.
But that should be the general idea.