It can be, when it means a want or need. It can also be a verb, to desire (to want).
"I want [desire] you."
desire or an adjective you can use would be "superfluous" If you're looking for a noun, I would call something you want but don't need a luxury.
It means to be obsessed with something.
A Desire
A Desire
take, require, expect, demand, involve, ask, desire, command, postulate, call for, necessitate, want
Need is something you have to have, a requirement for survival. A want is a desire and a desire is just a strong feeling of wanting.
By definition yes, said person could be lusting to be in a relationship. Lusting can be defined as, a strong desire for something. So if you crave being in a relationship and have a strong desire for it, or the person you want to be with, then yes you could call it lusting. It doesn't always have to necessarily be a sexual desire.
a strong desire is when you want some thing very bad
Something that you want or would like to have.
want or desire