I started out playing 2nd edition, and have since played all editions of D&D (some, like 4th, for only a single session, others like 3.5/Pathfinder for a couple of years), and Lamentations is my favorite of them all.
First off, from a rules standpoint, I would say 3.5 and LotFP are at two ends of a spectrum:
3.5/Pathfinder really encourages min/maxing, rules for everything, lots of skills, lots of tinkering and options around character creation, big stat blocks for creatures, as well as tactical, detailed combat and the idea that the PCs are heroes that should only die in the most extreme situations (and often have a chance to be resurrected). Some people are really into this.
Personally, I get bored during the lengthy combats, I don't care about customizing every one of the hundreds of digits on my character sheet, and I really dislike bloated skill systems. (Also, I hate rules lawyering - when a player is trying to teach the GM how to handle a situation, I consider that a problem with the ruleset.)
LotFP has little in the way of character options mechanically speaking. What's important here is how the player feels like playing the character. You could have a party of fighters and each player would be encouraged to come up with their own idea about what's up with their character. That said, what's most important is player agency - if your character has a low intelligence, it doesn't mean you can't solve the mystery or the puzzles presented in the adventure - all players should be working hard to figure everything out, or else they will all surely die!
The rules are very streamlined and easy to learn, run and riff on. Rather than checking every rule you don't know, just make something up (maybe a chance of success on a die roll) and keep going.
The PCs are not necessarily heroes, but greedy transients, willing to risk body and soul for a bit of coin. They have a high chance of dying or worse while going about this business.
Again, I'm not trying to bash Pathfinder here (I'm still playing in a 2 year campaign myself), but frequently I feel like the rules of that game get in the way of the fun or what we're trying to do, whereas in LotFP, the rules get out of the way and let us play efficiently and have a lot of fun.
That said, I believe 5th edition is a solid set of rules and you could easily adapt LotFP modules to that ruleset if you prefer that (I mean, you could to 3.5 as well, honestly, but that'd be even more work).
The modules are the most important element of LotFP, and I agree Ed's post above - read Better Than Any Man and/or The Doom-Cave. If you like the possibilities you find within those modules, then LotFP may be a good fit for you!