She's kinda weird in terms of series lords since losing her doesn't entail a gameover like every other main lord or lord-like in the series.
She's also odd in that she's the only lord in the series who can change depending on what you do in the game since you ultimately have 6 different possibilities for her to turn out into which makes rating her even harder since you have to determine who the mother is (and in the Avatar's case, the Avatar's chosen loadout). In comparison, not even Seliph has that much possibility in starting variable given that his loadout is mostly fixed to his parents Sigurd and Deirdre (the former of whom will likely ram his level cap of 30 and the latter has barely half a chapter to do anything and can't even promote). Admittedly Leif has a bit more leeway in terms of inheritance but in his case he isn't a main lord or even holy weapon user in FE4. Also his parents both leave by around the end of chapter 3 anyways so they'll both be lucky to promote before they leave (actually, now I'm curious as to what happens when it comes time to recruit Lief if you had let Finn die before the timeskip, let both of his parents suck and die, and didn't bother to pair Raquesis and/or also fed her to the wolves or paired her to Arden while both are sittin' on the bench; most likely a very annoying Leonster rush). And none of the other lords even have an opportunity to be different given that they almost always join at the very start of their games/parts.
As for actual game performance, since she joins after chapter 13 no questions asked, she will always have the opportunity to join in on the active party without slowing you down too much unless you perform some kind of crazy minimalist screwage to insure her base stats are as low as possible (even then they'll be better than Chrom's base stats which he'll have if you're going for said screwage). Chances are though that she won't be stat screwed and her lower level will let her gain levels quickly enough to match or surpass her parents and the team (barring Donnel if you're using him). Moreover her version of the Falchion is actually really good in of its own right (comparable to a Silver Sword in might and +5 in crit chance, has Dragon and Dark Dragon effectiveness, usable as an item to heal HP, and has infinite uses) though it doesn't get better like Chrom's does. Her version of the Lord class has slightly different caps than her father's by having higher speed and skill over strength and defense but given what children inherit in terms of caps, this is mostly a moot point outside of the generally higher speed. In terms of skills, outside of Charisma which eventually gets outclassed by later skills, the Lord's skill set is amazing and the fact that Lucina can supplement that with stuff like Galeforce or Astra makes it all the better. The rest of her father's classes aren't really all that impressive though as Aegis, Defender, and Luna are okay and Bowbreaker is good if you've got a flying class but Tomebreaker is also needed to assemble a not Iote Shield and without that you're only bypassing the less threatening of the two flier threats.
In terms of inheritance, her best mother is the Female Avatar (passes down all the standard female classes including the Myrmidon, Mercenary, Pegasus Knight, and Dark Mage class trees; Morgan also appreciates Rightful King)>>>>>>>>>>>Olivia=Sumia (the former may only pass down two class trees but they are Myrmidon and Peg Knight, she also gets even more Myrmidon-like with her gains and caps which is good for maintaining doubling capacity; the latter passes down three classes but Knight overlaps with Cavalier and Cleric is kinda useless to Lucina; Inigo also appreciates Rightful King and Cynthia doesn't have too many good fathers to choose from)>Maribelle (gives really high Luck to Lucina and Brady which will be nice for Miracle procs and Brady will appreciate Rightful King for even more Miracle but beyond that, easy staff experience later on, and potential Galeforce Maribelle is kind of a wash)>>Sully (only two additional class trees for Lucina and no Peg Knight in sight is kinda underwhelming and the stat caps make her more like her father than otherwise; Kjelle will still get three class trees out of the deal and Aether but she wont appreciate the Cav overlap at all)>>>>>>>>>>>Random Female Villager (Lucina gets absolutely nothing, she loses, good day!).
So at the end of the day, Lucina is solid for the most part (barring a RFV pairing and/or a bad Chrom which makes her terrible or an Avatar pairing which makes her fantastic) and comes usable right out of the box and with room to grow in barring shenanigans like Lunatic or Lunatic+. However, due to her lack of vitality, she's almost just as easily replaceable with any of the Marths (especially DLC Marth who comes with a free Aptitude skill and the Male Avatar's reclass set plus lord-alike Lodestar which even allows him to equip Lucina's Falchion (not certain about Chrom's)) although she will still have Supports over any of the Marths.