We'd call the arrangement "a marriage of convenience". As for lover/mistress, a mistress is always "the other woman" in an affair. A lover has a more general meaning, can be either gender, and doesn't always imply an extramarital affair.

I would think that if a man marries a woman for personal interest, that perhaps there must be some love involved. Otherwise, there must be a good reason. A lover can be someone your are involved with-either your partner or someone you are having an affair with. A mistress CAN be the same thing but this is only a woman that you are having an affair with, whereas a lover can be a man or woman. Hope that helps!