Fighters in old-school D&D are powerful, but they're mechanically pretty dull. You get...better at hitting stuff, and better at avoiding death and dismemberment. That's it.
This is one potential way to make them more interesting and adding nuance to how they play in combat.
You know how "specialists" in LotFP have skills that you can improve by filling in pips on six-sided dice as they level up? What if fighters had weapon skills--that only they have access to--based on the properties of whatever weapon they happened to be using?
It would work like this: when you roll a d20 to make an attack role with your fighter, you also roll a d6 for their weapon skill at the same time. If the d20 indicates a hit and the d6 roll is equal to or less than the number of pips they have in the corresponding weapon skill, the attack is a hit and deals damage, plus the weapon's special property comes into play.
Some examples of possible weapon skills/properties:
Assail -- when this weapon property activates you can make a second attack against the same foe, but you do not get to roll your weapon skill die for this bonus attack.
Weapons that might have this property: dagger, sling, quarterstaff
Brutal -- when this weapon property activates you can roll twice for damage against your foe and take the higher result.
Weapons that might have this property: battle axe, maul, claymore
Defend -- when this weapon property activates your armor class improves by one point until the start of your next turn.
Weapons that might have this property: poleaxe, dueling sword, main gauche
Hack -- when this weapon property activates you get a +2 bonus to your next attack against the same foe.
Weapons that might have this property: sword, axe, falchion
Stagger -- when this weapon property activates you cause your foe to drop one spot lower in initiative order. (I'm assuming d6 per side initiative.) If your foe's initiative drops below 1, it is stunned for one round and must roll initiative again on its next turn.
Weapons that might have this property: flail, mace, warhammer
Weaken -- when this weapon property activates your foe's armor class gets worse by one point.
Weapons that might have this property: spear, planson, longbow
I'd assume that fighter's start with one pip in each weapon skill, since they're trained in using all weaponry. Not sure about the rate they should gain pips to spend on improving those skills yet; this is all untested material in the spitballing stage.