The main issue with LoI is that it's designed as if it's a 2D game even though it's a 3D game, with the solid segregation of foreground and background you'd expect from any regular Castlevania game translated to 3D where it doesn't work at all. In-room detail is folded out of the walls, but is completely non-interactive [to the point you can't even jump over it], and the levels are treated as if they're tile sets in a 2D game rather than actual structures. That needs to be the first thing to change: everything inside a room ought to be possible to jump on or over, and more things should be breakable or possible to examine. I wouldn't mind levels a third of the size if they're not made of identical rooms. Level structure should focus on exploration, but with far greater emphasis on rooms joining together rather than walking in a direction until you can't go that way anymore and then doubling back.
Whip-jumping should just be flat-out removed, it really isn't that interesting a mechanic. Using the whip to swing from things would be nice, but just using attack as a jump button in some situations is silly. If it has to be there, have it triggered with the jump button.
Equally, the camera needs fixing: At very least, there needs to be a camera location at each end of any given hallway, since LoI could only deal with this by never spawning enemies in a corridor if you were walking 'into' the camera. Either a DMC-style system of many fixed cameras or even a proper 3D camera would be much better.
Enemy design should focus on a small number with a lot of abilities rather than a large number with a couple each; that'll make combat more interesting, since you won't just be dealing with the same attacks over and over.
Story-wise, the whole aspect regarding the crusades is silly: not only is the game set a year before the Crusades even started, it seems pretty daft that the church would go for the holy land with perfectly serviceable demons to fight right there in their own back yard, and Leon's renouncing of his title just seems a cheap way to heap more arbitrary tragedy on the character. So, have Leon go with the church's blessing and keep his sword, receiving the Alchemy Whip as well, and let him switch between them as he likes. The sword would be relatively weak but fast and with a wide variety of moves while the whip would be slow, strong and have a bunch of extra combat abilities like wide sweeps or the ability to grab and throw enemies. Ditch the system of learning moves when the game feels like it; give Leon most of the core techniques immediately, with the rest bought from Rinaldo as 'technique books' or something so you can see what Leon's capable of immediately; you shouldn't have to earn even the most basic abilities like Perfect Guard and the default whip combos.
Don't bother enchanting the gauntlet unless Leon's going to start off with a Relic worth using, otherwise hold off on that cutscene until he's been handed a couple. In Lament, the orbs, relics and gauntlet never even came into play during the unbelievably long first level, and it takes forever to build up a decent collection of orbs. They might be cool, but they're not cool enough to be a reward for two hours of wandering around. Also, tighten up the Gauntlet's ability to interrupt the run-out animations of other moves; it's pointless having a guard move if you have to take hits all the time anyway because all your moves have tons of idle frames tacked on the end. Another idea might be to allow Leon to use the gauntlet to catch and throw back enemy projectile attacks, or use MP directly to do so.
The story ought to play more of a role in the stages; not necessarily cutscenes, but shorter stages with stronger themes would work far better; for example, if House of Sacred Remains is going to have an icky biological boss, why not have the rooms slowly shift from stone and metal to flesh and blood as you get closer to it, and the enemies shift similarly from more normal things to boss minions and even the rooms themselves?
Reduce the number of torches and increase the heart pickups to 5 and 10 rather than the default drop being 1. Make it so there's a given item in each candle, not just a single heart or a single coin in dozens of them; after all, they're no longer going to be the only interactive scenery, so we don't need as many. Have Leon run faster, and generally move a little more quickly.