Manipulating the input mesh with Translate, Rotate, or Scale may be helpful with some features to the get the result you want.

The orientation of your model will influence how the lattice pattern generates in the design space. Adjusting the orientation of your part is a tool you have to influence the aesthetics of your lattice.

This example uses a Voronoi lattice type. Note how Voronoi's secondary pattern is more prominent in the Y rotation in this geometry. (No other surface controls were used in this example.)

The orientation of the part matters when using the Apply Base feature.