You should be fine. I played Luigi's Mansion: Dark Moon long before I played the first game...Well, the 3DS port. I don't recall the plots tying together in any way other than the fact that Luigi already understandably knows Professor E. Gadd in the second game.
Tl;dr: Play them in any order you like until we learn otherwise.
Currently playing: Mario & Luigi: Bowser's Inside Story + Bowser Jr's Journey, Ys VIII: Lacrimosa of Dana (Switch)
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Topic: Which luigis mansion game should I play first
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