There was an interesting question on MO which OP removed by some reason. Here is a (more or less) equivalent form.
Take a finite cartesian product of finite linear orders, and remove top and bottom. What is the homotopy type of the obtained poset?
When all linear orders have two elements, this is a sphere. In that question, it was conjectured that if at least one of them has more than two elements, then it is contractible. I think in fact from $3\times2\times2\times2$ one gets a (thickened) 2-sphere but I am not sure.
In general, is it known which homotopy types may occur when one removes top and bottom from a finite lattice?