Minimum current or power for Arduino Mega
The Arduino's voltage regulator is rated for a suggested input range of 7 to 12 volts. Automobile power will range from slightly below 12 volts to over 13 volts, so stepping it down to 7 volts is a good idea.

Looking at the data sheet it doesn't say how much current it draws. Since it uses a linear power supply it will likely draw the same amount of current regardless of the input voltage, and simply waste the power from a higher input voltage as heat.

The power from a car cigarette lighter should have plenty of current, so your proposed setup should work just fine. Is your 7 volt supply regulated?

Note that you could also use a "buck" style switching power supply to feed 5 volts directly into the 5V line. There are several buck style power supplies on the market for less than $10 US that will provide up to 3A of regulated 5 volts.