Philosophy of love and sex

It can be argued that love, sex, and lust are neither sufficient nor necessary for one another taken singly or in pairs. For example, while it is true that one can have love, sex, and lust together, it is also easy to imagine cases in which there is love without either sex or lust, or cases in which there is sex without love or lust. The combinatorics are straightforward, as the following table demonstrates (where a term appearing in parenthesis indicates its absence from the personal/social relationship.)

love          sex              lust
love          sex            (lust)
love          (sex)        lust
love          (sex)     (lust)
(love)    sex      lust
(love)    sex          (lust)
(love)    (sex)    lust
(love)    (sex)    (lust)
Put another way, the above table exhausts the range of human personal/social relationships qua love, sex, and lust.

Give an example from popular culture (movies, tv, celebrities) or literature of each kind of personal/social relationship. Are some of these examples better than others with respect to human flourishing? Are some of these kinds of personal/social relationships to be avoided for the sake of human flourishing? Explain the features of the personal/social relationships which either contribute to or detract from human flourishing, and rank all the kinds of relationships accordingly. Finally, what implications do your answers to the above questions have for understanding the relationship between love, sex, and lust?