What is lattice enthalpy?
There are two different ways of defining lattice enthalpy which directly contradict each other, and you will find both in common use. In fact, there is a simple way of sorting this out, but many sources don't use it.
I will explain how you can do this in a moment, but first let's look at how the problem arises.
Lattice enthalpy is a measure of the strength of the forces between the ions in an ionic solid. The greater the lattice enthalpy, the stronger the forces.
Those forces are only completely broken when the ions are present as gaseous ions, scattered so far apart that there is negligible attraction between them. You can show this on a simple enthalpy diagram.
For sodium chloride, the solid is more stable than the gaseous ions by 787 kJ mol-1, and that is a measure of the strength of the attractions between the ions in the solid. Remember that energy (in this case heat energy) is given out when bonds are made, and is needed to break bonds.
So lattice enthalpy could be described in either of two ways.
In the sodium chloride case, that would be -787 kJ mol-1.
In the sodium chloride case, that would be +787 kJ mol-1.
Both refer to the same enthalpy diagram, but one looks at it from the point of view of making the lattice, and the other from the point of view of breaking it up.
Unfortunately, both of these are often described as "lattice enthalpy".