How do you know whether to use a lone pair or a double bond when drawing a lewis dot structure?

Well that depends on the central atom. Remember each bond indicates another electron that is being shared with the central atom.
So CO4, carbon would be your central atom, with the 4 oxygen around it. There would be no double bonds because carbon only requires the 4 electrons provided by the oxygens, because of its location on the periodic table.
Nitrogen on the other hand is different. It's found in group 5 (5V) and has 5 valence electrons on its outer shell. So NO4 would have a central Nitrogen atom, with 3 oxygens providing a single bond, and one oxygen providing a double bond, because Nitrogen needs 5 electrons!
We learned it like this, the atom brought x amount of electrons to the party, x representing the valence electrons, and must leave with x electrons. It's silly but it works!
I hope I was able to help and clarify a few things up!

The answer options is d