The included models in LTSpice do not include reverse breakdown. In order to model the reverse breakdown "vrev" can be specified in the diode model. For this example, create a new schematic and call the diode "mydiode". Insert the .model directive to add the reverse breakdown. Below, I used all the standard parameters for the 1N4148 and added vrev=50. The vrev specifies the reverse breakdown at -50V. Many other diode properties can be defined in the model including the non-linear characteristics of the breakdown.
Forward and reverse breakdown and current limitations can be modeled by using a more sophisticated model. Using the model below, forward and reverse current limiting can be observed.
.model mydiode D(vrev=40 Ibv=20nA BV=40 Ibv=1e-10 Is=1e-7 Rs=10 Tt=2n Ilimit=5mA Vpk=40 Revilimit=5mA)