Tough call. Haven't played enough of 3 yet so I feel I can't really comment too much on it but it may end up being my favourite once i've completed it!
Between the first 2 it's really close but I'll just about go with the 2nd. I liked the different mansions, the puzzles and the bosses all better than the first game - It just felt like it had more overall variety. The 1st one wins on originality, atmosphere and charm for me though (that and the portrait ghosts were really fun - the one disappointment with the 2nd game was the exclusion of them!). When it comes to longevity this is where the original falters, the game is unfortunately quite short and other than completing it again there's no real reason to re-visit. At least LM2 has more collectables and challenges that mean you can come back to it and replay some of the missions.
In the end there isn't much between the 3 of them - they're all really fun games that I would recommend to anyone!