lsd= limited slip differential, it's a device that doles out equal amounts of power to both of the front wheels, which helps to eliminate the problem with cars that don't have it. From a launch, a car without lsd will have one front wheel with no power going to it, and the other has all the power, this causes that tire to lose grip so relatively little power is mkaking it to the pavement, also the car will tend to torque steer(on side of car is being pulled more than the other cause the car to act like it wants to turn) under heavy acceleration. an LSD will put equal amounts of power to the pavement through both tires, allow both tires to accelerate at the same time eliminates torque steer, and it also allows relatively more power to be transfered.
In short, with two similarly odified and tuned engines in the same model/trim level car, and similar driver skill, the one with LSD will be quicker off the line.