lattice enthalpy

As one of my students proclaimed with excitement, "aha, so it needs energy to keep them apart, then when they stick together that energy is released!"

That would make sense, it would need more energy to keep things apart if they are more strongly attracted to each other.

To my embarrassment, somehow I never really questioned why bond making is exothermic during my education. It just seemed reasonable that it's the opposite of bond breaking which should be endothermic as it takes energy to pull things apart. I'm interested to read others' thoughts.

Why does a more exothermic value for a lattice enthalpy mean that there's a stronger electrostatic attraction between the oppositely charged ions? Why is energy given out when bonds are made exactly?

Because if there's a very strong attraction between 2 ions, theyre going to want to form, because it's favourable for them to do so.

Hence when they come together, energy is released and this is why it is very exothermic.

Think about it. If 2 ions are greatly attracted, theyre not going to need any external energy to draw each other closer, hence it cannot be endothermic in this particular case.

I understand that they'd want to form and that they don't need energy to do so, but why do they release energy?

Bond formation releases energy and bond breaking requires energy. Why?
Bond formation makes the participants more stable so they lose energy. It is the same as you losing energy and relaxing on your sofa.