Lust is defined as a passionate desire for something.
a passionate desire for something.
"a lust for power"
synonyms: greed, desire, craving, covetousness, eagerness, avidity, cupidity, longing, yearning, hunger, thirst, appetite, hankering
"a lust for power"
Greed is defined more as selfishness.
One can lust over things even strongly without being selfish. For example if I craved or lusted over alcohol or drugs, it doesn’t make me greedy. Maybe I share my alcohol and drugs openly... Greed is more hoarding for one’s self, more than one needs while not sharing or helping others. Similarly one can be greedy without necessarily listing over something.