Do you think Lupin and Lily Potter were romantic?

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i started a discussion a few days ago wondering why james and Lily potter chose Wormtail over Lupin to be the new Secret-Keeper. So here is my theory on why they did: james thought that Lupin and Lily may have once been romantic or were attracted to each other and so he was too jealous to trust Lupin. My basis for that theory comes from 2 things. 1) The way Lupin talks about Lily in the 3rd movie in such a fond way. 2) The parrallel between james Potter and his friends And Harry and his friends. James and Lily are like Ron and Hermoine and Harry is like Lupin. So what do you think of that theory?