In Lamentations of the Flame Princess, PvP combat is obviously not meant to be a focus. Sure, PCs attacking one another isn't entirely out of the question, but I think the game is generally meant to be a cooperative experience as far as the party is concerned. If players wanted to make their characters fight in a tabletop RPG just to see who was tougher or to enjoy some kind of deep tactical experience, they would almost certainly choose another game. So when I talk about balancing character classes in LotFP, I'm not talking about giving them an equal chance of beating each other in a fight.
I'm also not necessarily talking about giving different character classes equal utility or damage-per-round or body counts in combat. Combat is just one of many parts of the game, and far from the primary focus. It can be a ton of fun, and it has its place, but battle is not the only deciding factor in determining how useful a class is to party success. Some classes might have little to contribute in a fight but make all the difference in other situations.
So when I talk about whether or not one class is balanced against another, here's what I'm talking about: Whether or not Class A and Class B have roughly the same overall utility to a party across the entirety of the typical adventure. If Class A can contribute to the party's success in multiple situations but Class B is only useful in one specific situation and just dead weight in all others, then the classes are unbalanced. They don't have to be good at the same thing (or else why have separate classes at all?) but they all need to be good at something helpful that is likely to occur more than once every leap year. And if Class A could do everything Classes B, C, and D could do, but better, that would be even more unbalanced. Either everyone would pick Class A so they aren't weakened to a needless degree, or everyone would pick anything but Class A in order to actually have some kind of meaningful challenge, or everyone would still pick each of the classes but all of the Class B/C/D people would resent the Class A people and a game that was meant to be fulfilling becomes stressful and dumb.
The nice thing about OSR games like LotFP is that characters tend to be able to contribute to the adventure in ways that have little or nothing to do with their character classes. Any class can pull a lever or carry items or solve a riddle or ride a horse or throw down some flaming oil and run away or cut the ropes on a bridge or sweet-talk the mayor or...you get the idea. This makes class balancing less of a concern. Still, I don't want to be the guy who presents one class that's Superman and another that's Jimmy Olsen and try to convince people to be Jimmy. I mean, LotFP is a horror game, so if bad stuff is inevitably going to happen to everybody (or at least likely to happen, depending on how smart and skillful and lucky the players are) let's at least not force anybody to be an incompetent jackass unless that's the character they want to play.
For me, balance in LotFP isn't really about making everybody feel powerful and special. It's about making things fair while still offering variety. Maybe that's a small distinction, but I think it matters, and that's why I think class balance matters. If something bad happens to a PC on an adventure, I think it should be because someone screwed up while adventuring and not during character creation. If you want to introduce something unfair to the game, I think you'd be better off doing it through an adventure or item and not through a class.
Unless you wanted to create a purposefully-awful joke class, and present it to the players as a joke and not as a balanced class. That might be cool.