We just moved into a new house this winter, and although we are renting, are responsible for all the lawn care. The grass is terrible, non-existent in some places. The soil is very sandy (we are only a few miles from Lake MI), there are lots of trees (so very shady), and we are trying to figure out the best way to have green grass this summer. DH wanted to call someplace like TruGreen and get them to just fertilize the heck out of it. He did call them for an estimate, and also to ask what exactly they apply (2-4-D, nitrogen, and something else). He also found another local company that uses a chemical called Dithiopyr. We looked at the safety sheets for it, and found there really isn't a whole lot of info on it. Frankly, neither of us is crazy about using chemicals (and the 2-4-D isn't even an option, as it's extremely toxic), but we don't really know what to do to fix the problem. I suspect that the real problem is that the soil is just not very good, and that the previous tenants' dog damaged the grass's root systems, causing large sections of the grass to die out. I would appreciate any suggestions or links to less toxic, natural lawn care options. Thanks!
If your soil is very sandy then it is possible that fertilizer will help; however, it is also possible that your grass is not growing because of the trees. I have seen grass grow on incredibly awful soil left behind by builders on the lot across the street without any fertilizer, other than what was applied at planting. On the other hand, I have some very shady spots in my lawn that grow lovely green grass in the spring and fall if I reseed every year, but are almost bare through the summer, when the overhead trees are fully leafed out. (I've read that you should apply less fertilizer to grass in shady areas, though I'm not sure if that's to protect the grass or just the environment.) Or if the trees in your yard drop needles you may also have very acidic soil. I would start with a soil test to make sure you know what's needed, then try a shade-tolerant grass species. You can usually get good recommendations from your state extension service.
There is some extremely deep shade in my north-facing front yard that a wise previous owner just filled in with shrubs and groundcover. If you're considering going to the expense of hiring a lawn company I would consider planting something besides grass in the shadiest areas, if your landlord will allow it. (Sandwiching a narrow strip or area of grass between "flower beds" may make this a more acceptable idea. Landlords also like the words "drought tolerant", especially if they are paying the water bill.) If there's a garden club in your area they may have a spring plant sale where you can buy good local-hardy perennial plants cheaply from people who are dividing stuff from their own yards. Or you could always ask on freecycle.