In Marlowe's Doctor Faustus, the theme of covetousness in found in Faustus' greed for money and magic—which will afford him great power.
Covetousness is a form of greediness. Covetousness is defined as:
inordinately or wrongly desirous of wealth or possessions, or eagerly desirous
"Wrongly desirous" may mean that one wants what does not belong to him or her—this kind of person might steal or cheat to get what he/she wants. In Doctor Faustus' case, his desire extends to a willingness to sell his soul to the devil.
After Doctor Faustus has sold his soul to the devil, he is visited by Lucifer, and then the Seven Deadly Sins. Covetousness is one of these sins. It speaks to Faustus:
I am Covetousness, begotten of an old
churl in an old leathern bag; and, might I have my wish
I would desire that this house and all the people in it
were turned to gold, that I might lock you up in my good
chest. O, my sweet gold! (128-132)
The connection here is that "Covetousness" is a deadly sin. This is something that Faustus has chosen to embrace. The sin is deadly, not in this case because it takes Faustus's life, but in that moves Faustus to freely give his soul away for covetousness. The main connection being that it is one of the paltry rewards Lucifer holds out to Faustus after he has sold his soul.
When Lucifer asks Doctor Faustus how he feels about what he has seen, Faustus notes that it "feeds" his soul. Lucifer explains that hell holds "all manner of delight," and Faustus expresses a wish...
O might I see hell, and return again,
How happy were I then! (181-182)