Are the attractions among ions within a crystal lattice are weak or strong?
These are strong, and not constrained to molecular boundaries.
An isolated cation in an ionic lattice is electrostatically attracted to every other anion in the entire lattice. Of course, the cation is subject to electrostatic repulsion from every other cation, but if you sum up attractive and repulsive interactions, which can certainly be done quantitatively, a net attractive force results that binds the entire lattice together.
Ionic solids with greater than unit charges, carbonates, phosphates, oxides, tend to be insoluble. This probably reflects the greater electrostatic force of attraction made possible by binary or tertiary electrostatic charges.