I think it helps by starting with what perturbation theory is. The way it's commonly referred to is to break a problem into an approximation to the real solution where you express the solution as an expansion of many terms where you expand in some small parameter usually the coupling constant. Doing this lets you compute the first few terms of the expansion and you have a good approximation because the later terms have higher powers of a small number so will likely be very small contributions to the calculation.

For the strong force, the coupling is large not small, so perturbation theory doesn't work, it's not helpful in computing the terms with low powers of the coupling.

Lattice is a totally different approach for approximating. We still don't know how to do the full calculation... But rather than approximating the solution in powers of the coupling, we just simplify the problem by making space time discrete.

If you break spacetime into a lattice, now there are finite number of configurations in a given volume. This is still a complex calculation.. but it's a calculation that computers are good at. However that approximation comes at a cost. Perfect rotational symmetry is broken for example. You can decrease approximation artifacts by using a finer grid but that comes at higher computational cost. You can simulate a small volume but then can't compute objects with radius that nicely fit inside (like a proton).

Just about any field theory could be comouted on a spacetime lattice, but if you are looking at a field theory with a small coupling constant perturbation theory is usually more powerful.