How does Dating work in Buddhism
A wise man should avoid unchastity as (he would avoid falling into) a
  pit of glowing charcoal. If unable to lead a celibate life, he should
  not go to another's wife. - Dhammika Sutta


A layman is not expected to lead a celibate life. What you are expected as a Buddhist is to avoid sexual misconduct.


  Is it even possible to have a girlfriend/wife without lust?


Yes, but not necessarily for the good. ex: marrying to get citizenship, marrying for money, power, marrying to cover up sexuality etc.

A good example would be a married man becoming an Anagami later. He can still live in the lay life, but girlfriend/wife will merely be ceremonial positions. He will just treat her as a sister or a friend.