"I am reading by the red lamp."
Translation:A piros lámpánál olvasok.
No, because "the red lamp" is not the grammatical object of "I am reading". If it were, the English sentence would be "I am reading the red lamp", and the Hungarian could be "A piros lámpát olvasom".
The phase "BY the red lamp" ("a piros lámpaNÁL") has an adverbial function; it's a sort of modifier adding extra information to "I am reading", which could have stood alone as a full sentence. That sentence has no definite object (no object at all, in fact), so the Hungarian equivalent uses the indefinite form "olvasok", not the definite form "olvasom", and that doesn't change when we add back the modifier.
As I understand it "A piros lámpánál olvasom" is a valid sentence, but it would be translated to English as "I am reading IT by the red lamp", where the thing you're reading explicitly appears in the sentence (though only as a pronoun, so it doesn't convert any information about what it is); the sort of thing you might say in response to a question like "Where are you reading the letter I sent you?".