Lugan is the friendship pairing of Logan and Lucy on Big Time Rush. The two are good friends, but they don't like each other in a romantic way, both Logan and Lucy have other crushes.
In Big Time Rocker, Logan (and the other guys) appear interested in Lucy. In the episode, though, they never talk because Logan ends up spending his day with Camille.
In the episode Big Time Secret, it shows that Lucy and Logan have become friends somehow. This is confirmed even more when Lucy helps Logan figure out what's going on between Kendall and Camille.
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- Logan is playing games at Lucy's room along with the guys and Camille.
- Lucy tells Logan that she didn't know Kendall and Camille were dating.
- Logan gets Lucy to spy on Kendall and Camille for him.
- Logan trusts Lucy.