how long would it take to extract power from lemons to get enough a charge and store in a car battery to power a standard 300 watt computer for 10 mins
Lemon batteries are actually powered from the metals not the lemon. The metals are not much different from the metals in alkaline batteries, which would work much better. You would need about 3 D cells, but 8 Cs would be simpler to charge a 12 volt car battery. If you use metal and lemons, you would need more metal than that, maybe a pound or two. Zinc and copper sheet metal may be the easiest way to try this. Replace the sheets as you use them up (they will get discolored and brittle; this is similar to iron rust). You need to arrange lemons in series to get 12-15 volts to charge a car battery. You need an inverter to convert the car battery from 12VDC to 120VAC to plug in the computer. Expect to spend around $80-$120.