... thereby influencing the handling of the vehicle

The LSD differential enables traction force to transfer traction force from one wheel to the other.
To what extend this happens, depends on the chosen configuration, momentary speed difference, vertical load on the individual tires and ingoing torque.
Front wheel drive or rear wheel drive

In the differential menu one can select whether your vehicle is FWD or RWD.
The main focus of LapSim has been on RWD, because the vast majority of race cars are RWD. So certain functions are not available for FWD.
Transferring incoming torque to locking force

To what extend the ingoing toque of a LSD is used to transfer traction force, is determined by the ramp angle of the LSD.
The smaller the ramp angle, the bigger the percentage of ingoing torque which is used to transfer traction force.
Independent of the incoming torque

The preload value of a limited slip differential is the amount of traction force the differential can always transfer, regardless of the ingoing torque.

Negative preload
It is possible to specify a negative amount of preload in LapSim. This means the differential is open, so no force transfer, till a certain amount of ingoing torque is reached.
Locking force dependent on speed difference

Finally it is possible to add a viscous part to the differential.
The traction force transfer is in this case only dependent of the speed difference over the differential. LapSim assumes a linear relationship.
Ability of the differential to generate locking force

The percentage of Limited Slip Differential part of the differential is determined by the ramp angle (drive and brake), the amount of friction faces and the friction coefficient of the plates.
The issued "friction coefficient" is a resulting factor out of the parameters specified above.