What force holds the lattice structure in place in a crystal?

At the end it depends on the type of crystal.

There are ionic crystals (like sodium chloride), covalent cristals (like diamond) and metallic crystals (like aluminum).

The context of the question may tell you if it is referred to one type of crystal or other.

I gues it may be about salt compounds, which are ionic crystals. In this case, the force that holds the lattice structure in place in a crystal is ionic (electrical attraction between cations and anions).

In the other two cases, the force is covalent bond in one case and metallic bond in the other case.