how to vary the threshold voltage of a MOSFET for simulation in LTSPICE
Spice model decks typically have different model instances and names within them.  It's simply a matter of calling the appropriate model for your transistor.  You will have to open the model file and find the calling instances for the different models within it.

Each foundry will typically have a different calling name so a general statement is not not possible.

For example in one foundry for NMOS transistors there are ne,ne3,ne3i,ne5,ne5i,nei models in the sub-sub- directory.

the ne has this at the top 


".subckt ne d g s b w=1e-6 l=1e-6 ad .... "


which in turn is called by another file with this .


".include ./models/bsim3v3/ne.mod"


And then within the Spice instance of the model this is called:


NOTE: this is not LTspice but how spice simulators run in general.  LTSPice will implement some variation on this.  But the nested/hierarchical nature of the library calls are a fundamental feature.

The calling sequence can be confusing when there are different process splits and options.  Fast-Fast, Slow-Fast etc.