You mean object space, local space is actually another word for tangent space(see: idtech). But you're right, object space normals can't be mirrored unless you have a special shader set up to do it correctly. Rotating your mesh(in your 3d app), or creating rotated instances doesn't work even if you have a shader that works…
Object space normal maps are absolute - they give the explicit normal that the high poly surface is facing in.* The low poly model doesn't have to do anything other than record that in it's UVs. Tangent space normal maps are relative - they alter the normals of the low poly model to point up/down left/right of the current…