A nut and a lead screw are usually purchased components. The nut and screw each have a rated load. Design a machine and calculate the load that goes through the nut. Do a simple analysis where the screw is beam elements. The load that the nut drives can be connected to the beam with a simple joint such as a spherical joint. Probe the Joint to measure the load going through the nut. Select the appropraite nut and screw size once you know the load.
The first thread on a nut takes the most load and each thread after that takes less and less. After about one diameter of length, there is almost no load on the threads. This is normal.