I haven’t thoroughly read the Labyrinth Lord rules, but—to my knowledge—there is no provision for fighting with two weapons. And I’m perfectly fine with that.
Even so, there are some advantages to it without any mechanical considerations. e.g. Using a sword and a dagger means that you have a dagger ready to throw and a sword ready for melee at the same time. No time need be wasted sheathing or drawing either weapon. That, however, isn’t the reason many people fought with sword and dagger.
The Advanced Edition Companion gives the old AD&D rule. I’ve probably argued against two weapon fighting providing a second attack sufficiently. Suffice it to say, I think a second attack is generally not a good way to model anything in most D&D-derived combat systems.
I’m leaning towards this: Attacks are resolved as if the character were only wielding the primary weapon with an additional +1 “to hit”. The player may decide each round which weapon is considered the primary.
The nice thing about this is that it doesn’t discourage using more unusual combinations—e.g. two scimitars—but it doesn’t encourage them either. Most characters will probably stick to sword and dagger except for style or expediency reasons.
As others have said before me, this is also a nice foil to the -1 to AC granted by a shield.