Lust is the succubus, and sin of sex, because as teens reach their 20s, they tend to get sexual urges towards the people they run into while also enjoying themselves too much while they were spending multiple minutes trying to make themselves cum. That's where lust comes in, to make sure they have a good time.
While some people have different kinks, others just need money, and sometimes get too addicted to sex that they don't know what to do what themselves. As for Lust's job, like how some of her sisters deal with people who want money, food, or to sleep, she helps people who want to fuck other people, until they get pregnant. However, if a human decided to make the succubus mad because of something they did, Lust will get mad, and curse them as she knows that she won't take it sitting down.