Covergence Study for Solid component and lattice component


Hi everyone,
I want to do a convergence study for two components ( 1st Solid component and 2nd lattice component) I have attached the pic of my components together in one picture for your reference.
First I want to do a mesh convergence for lattice to find out optimial mesh for the component with the same E and density values , Similarly I have to do a mesh convergence for solid component same like lattice.
My Question is after finiding the mesh convergence study what I mentioned above I have to make a covergence study regarding E modulus, In order to tell how much the E has to be reduced regarding the density of Lattice component to reach same behaviour of solid component. How I can proceed to do convergence study regarding E modulus that the LS block and Solid-block have same behaviour. A help would be really appreciated. Anticipating a good response for experts. Thank you .
Kind Regards,
Muthu.