At the worst she's at the top of low tier. At best, somewhere around Marth usually below. But I have heard people say that Lucina may have the potential to be better competitively than Marth
I'm absolutely of that camp. I genuinely think that post-1.1.4, Lucina absolutely has the tools to stand toe-to-toe with Marth at minimum, and potentially outshine him straight-up. And there are actually several reasons why.
The truth is, Marth's biggest advantage over Lucina isn't even his tippered smashes, because while yes, they are DEVASTATINGLY powerful, even the absolute best Marth players in Smash 4 don't hit those every time. (And below the top level, the VAST majority of Marth players I see don't even hit it most of the time, meaning they're better of just being Lucina by default.) Surprisingly, the biggest advantage he has over Lucina is his tippered
forward tilt, which is extremely fast and has a kill potential that is disproportionate from most of his tippered attacks vs. Lucina's blade. Marth's forward tilt can kill moderate-weight characters at 80-90% at the end of the stage, but Lucina's will almost never kill. This is the ACTUAL point of contention that might put Marth in a better category.
So, why do I disagree? Well, several reasons, actually. The fact of the matter is that 1.1.4 was a huge game-changer for the two of them in so many ways. Prior to 1.1.4, their hitboxes were very small and broken, which made spacing a nightmare. They also had TERRIBLE frame data on a lot of their attacks. So the fact was, Marth NEEDED that extra kill option and Lucina flat-out never even HAD it. So yes, prior to 1.1.4, I would say Marth was just better.
One of the most incredibly huge buffs they got was surprsingly to their jab, which was a frame faster (that's a BIG difference for jabs), and combined with the VASTLY improved hitboxes on a lot of attacks, they now have so many, many MANY more combo options than they used to have. As a result, the admittedly still-useful forward tilt can now often be supplanted by setups such as jab -> forward smash, which kills better and is safer because it's dead easy to hit-confirm.
Lucina and Marth's forward aerial is another MASSIVE factor in this, because prior to 1.1.4, it used to have an almost nonexistent disjoint. Now it's a fairly respectable forward air, beating out Sheik's in range and priority. Because of this, Marth and Lucina have AMAZING edge-guarding tools that have to be respected, making immediate kill options less important still. They simply dominate when edge guarding, so for many characters, just getting them off-stage is often enough.
Lucina is basically always going to rack up damage better than Marth, just due to the nature of the game. Even if the Marth player can hit all of his tippers, it's not always the best move because sometimes hitting the tip will ruin potential combo options such as Dancing Blade setups. Dancing Blade in and of itself will almost always do more damage when performed by Lucina. Again, this difference is often mitigated by a well-placed tippered kill move, but it is by NO means a factor that should be overlooked.
After the shield nerfing update, Lucina's attacks on shield have become slightly more safe than Marth's due to increased shield stun. While Lucina should always be spacing the same way Marth does, this means that she's less harmed by an attack that is slightly inside of where she expected.
Please don't misunderstand. I'm not saying "Lucina is always better end of discussion." I am saying that there's a definite discussion to be had, with points on either side. I personally think that Lucina's consistency and damage potential make her the stronger character, but I won't deny that a well-spaced Marth can easily blow her out of the water with his insane killing power.