How to power schmitt trigger in LTspice with negative voltage?
Is there any way I could modify the model to simulate my circuit in -5
  and 0V?


The circuit in your question shows power rails of -5 volts and 0 volts. That means the actual supply is 5 volts just as in any other more standard circuit of logic chips. In other words it makes absolutely no difference to your simulation.

You can simulate it with standard logic voltage levels and the sim result will be the same except the output will be 5 volts higher. If you need an output that is 5 volts lower (possibly to drive other circuits that are un-shown in your question) then put a 5 volt voltage source in series with the output.