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Brian has a special relationship with Lois. He realizes that he harbors romantic and sexual feelings towards her in the episode “Brian in Love”, but learns to accept friendship in lieu of a romantic relationship. But he seems to retain a certain amount of longing for her. In the episode “The Perfect Castaway”, Brian was married to Lois for a period of several months after they thought Peter and his friends were killed in a hurricane while fishing. The marriage was largely based on Brian’s ability to support the family financially in Peter’s absence by taking a job at the local Hummer dealership. Despite Brian’s desire to consummate their relationship, Lois insisted throughout their marriage on keeping their beds separated. When Peter unexpectedly returns home alive, Lois’ feelings for Peter rekindle and Brian and Lois divorce, as Brian accepts that Lois still loves Peter. Lois declares shortly afterwards that she was one day from deciding to finally have sex with Brian, to his great frustration. He additionally reveals that his attraction may go beyond skin-deep; in “Sibling Rivalry”, as Lois begins to gain weight, Peter comments that he is no longer attracted to her. When he asks Brian if he still is, he replies “I don’t care what she looks like, I would wreck that chick.”
(excerpt from the Wikipedia entry)