Thanks for the detailed explanation. I would suggest two things:
1. Change the boundary condition. Instead of using a fixed boundary condition at the bottom, apply a boundary condition like this:
Only in this way can you achieve a shear stress free deformation, and be able to test the Poisson's effect. The training material website in LS-DYNA does not say what boundary condition it uses, but I believe that's the one they use to get the exact 3e-5m lateral displacement. Here is what I got using these BCs.
2. Double-check your units. The input.k file (the keyword file) is the final input that is sent to the solver. So it is a good idea to check there whether your units are consistent. You can find the consistent unit system in here: https://www.dynasupport.com/howtos/general/consistent-units
The input file can be found by right click on your "Solution (D6)" --> "Open Solver Files Directory" ---> Open "input.k".
Alternatively, you can find it in the "LSDNYA Pre" tab --> "Write Solver file". In the keyword file, you can check what exact value you will input to LS-DYNA solver.
For example, in my input, I am using ton, mm, MPa, ms,