If there is nothing of value in the garden you can spray with Roundup. If there are plants your niece wants to keep then she needs to make sure that the Roundup does not get on them. You will still need to dig out all the roots in order to sow grass. Try and leave some of the ivy in a corner as it is a source of food and protection for birds and other wildlife.

If the ivy has thick woody stems, Roundup won't touch it, I'm afraid. The only answer is heavy duty digging to extract as much of the woody roots as possible, having cut it all down first. For stubborn roots which can't be shifted, treatment with SBK can be carried out - you'd need to drill or make cuts into the roots and then apply the SBK, but the product is like water and its difficult not to get it onto the soil used in this way.Too much of it present in the soil means nothing else will grow for a couple of months, so great care needs to be taken. Cover any roots treated in such a way with upturned pots, then move the soil back into position. This keeps the soil off the treated roots, enables you to find the areas again if they need re-treating, and prevents inadvertent planting on top of the poisoned root.