So "feel like it" is the answer, but "Do you feel like it" is wrong? That's arbitrary.
It is, but note that the German is very colloquial and leaving out the 'do you' comes closer to the tone of the phrase. So, I'd say both should be accepted, but 'feel like it?' is the better translation.
That's a good point; I actually had that thought later. (Since "Lust drauf?" omits "Hast du", and "Feel like it?" omits "Do you"--they're very parallel.) It is a better translation. But, given that the stated intention here is to teach German (and not necessarily just to native English speakers, presumably?), I disagree with counting "Do you feel like it?" wrong, because it fully captures the meaning, in perfect English.
I put "Do you want to", which I feel captures not only the meaning, but is also an incomplete phrase (thus capturing that element of the German).