Hi Smiley, You dont say what he used ? but assuming it was one of the modern weedkillers like 'roundup' the one good thing about most of these is that as soon as they touch the soil they are inactivated and are rendered harmless unlike the older chemicals which oured the ground for 6 months !
Ok, what i would suggest is that you buy yourself a very fine sieve, ideally about 1/4" mesh and one of those 'fish tail' type scarifiers, like a wire rake in the shape of a fan ?? Next, sieve some soil and also some peat and add some very fine sand as well, it doesnt really matter about proportions but roughly, equal parts peat and garden soil and sand, mix this together. Get some grass seed, if the lawn is quite good then get some that is without ryegrass, B & Q or any hardeware store will sell it !
First thing to do is to vigorously scratch the soil where the patches are just to scratch the surface, lightly scatter the grass seed on this scratched surface, dont be tempted to think if you put it on thick it will be better, it wont, to give you a guide about a handfull to a square yard is about right. When you have sown the seed, use your mixture to LIGHTLY cover it, a 1/4" deep layer is what your aiming for, just enough to cover the seed. Finally, get your fish tail rake and blend this 'compost' that youve added to the patches into the surrounding grass. Now given that we are having a warm dry spell, you must every day water these patches, do it lightly, preferably with a watering can and the seed will germinate in about 4-5 days. You must keep these areas damp for a while (about 2-3 weeks) by which time you wont notice the patches (hopefully) During this time, try not to walk on the patches and when you start cutting the new grass, dont cut it too short or you risk it dying out.
best of luck, hope this helps and that your landlord wont come around for a couple of weeks !! Lannerman.