Cutting left handed threads on a Haas Lathe is just as easy as cutting right handed threads.
The tools need to be mounted into the turret the opposite way round to normal, so left-hand tooling is used rather than right-hand tooling. Where we normally look at the back of a tool, with the insert facing the casting of your machine, we will now have the insert facing the operator when the tool is in the turret.
When this is done, there is one alteration needed in the program to cut a left handed thread:
Instead of running the spindle in the forward direction (M03 programmed), the program will now run the spindle in reverse (M04 programmed).
Another way this can be done, if there is no option to buy new tooling, is to use the standard tooling (right-hand) and program the thread to cut from the back of the thread to the front of the thread (from the chuck towards the tailstock end) i.e. the tool will be moving in the Z+ direction.
N.B. This will allow you to use the standard tooling, however there will need to be an undercut at the chuck end of the thread to allow the screw cutting tool to move to the start point for threading.