With the weight factor of your vertex group, you can control the strength or importance of your paintings. Factor „0“ means 100% importance and therefore zero thickness at the dark blue area. The red area has the same thickness as set at the Wireframe Modifier. Factor „100“ means the painting has zero importance and therefore the whole part has the thickness set in the modifier, no matter the painting.
You can play with the wireframe thickness, the weight factor of the lattice as well as the painting to create your ideal solution in terms of thickness. In the video I also used the subdivision modifier to create the smooth connections in the lattice structure. Keep in mind the minimal thickness of the Additive Manufacturing process you are using. Always adapt the design to the Additive Manufacturing technology and used material.