No, Lagging Tail does not affect moves like Magnet Rise because Lagging Tail only causes the holder to move last. Nothing more.
Analytic: Boosts move power when the Pokémon moves last.
Analytic does not affect Magnet Rise either.
Note that Magnet Rise DOES get affected by Gravity, Ingrain, the item Iron Ball, Snatch, and Smack Down. Those are the only moves that negate Magnet Rises effect.