my answer is.. yes to both.
lust to me.. is a desire, it's gonna be hard to be in a
relationship if you both don't desire each other. may not be
physical desire.. can be companionship etc.
if you don't think of each other subconsciously.. do you really
love that person? or maybe you're taking that person for
granted.
Yes to both questions
i agree with dumbdumb that lust is necessary in a relationship.
it keeps both parties interested in the r/s. lust is having intense
sexual desire and having sex is putting that intense desire into
action.
Having said that, i believe sex is not a key factor in
relationships. what's important is the companionship and the
intellectual connection with the other party. hence, i think r/s
can last without sex.