Yes, it is quite possible the chemicals in your lawn are harming your dog. There have been tests done that have linked certain lawn chemicals to cancer in dogs. This is a subject that requires more scientific research because much is unknown. In the meantime, it is wise to read labels and check that the chemicals you use are labeled “pet safe”.
If your dog has regular access to a lawn there is a good chance that he or she lays on it, rolls on it and chews the grass. Residue which clings to the fur will likely be licked off. The dog is more exposed to the lawn treatments than you are. Whatever is clinging to your pet will be tracked into your home and especially to the area where the animal sleeps. As there is no sunshine or rain inside your home to help break pesticide down it can remain in your carpet for years. Of course if your dog is an outdoor dog there may be considerable exposure to chemicals.
If you choose to use pesticides, be selective about which type you use and follow the directions carefully. The label will probably recommend you keep your pets off your lawn for a couple of days. It might not be a bad idea to bathe your pet often for a while. There may be a higher risk of illness for your dog if you use pesticide products on your lawn.
If you use fertilizers be careful about adding bone meal, say, and feeding your roses because dogs love bone meal and will likely dig down to get at it, consuming the fertilizer also. Be very careful your dog doesn’t have access to an open bag of any fertilizer.
It is possible to have a beautiful yard without the use of products which could harm your pets. Depending on where you live and what sort of soil you have, it could be partly a question of settling for less green in your lawn or perhaps planting a ground cover of another sort in some areas of your property.
Vinegar (use a garden sprayer) works well as a weed killer in gravel areas but it will kill grass also. Spray it when there won’t be rain for at least four days. It works well but must be reapplied, especially in rainy areas.
It’s a good idea to do some research and learn about the potential dangers of the various chemicals you might wish to use. Some organic products can cause irritation to the digestive tract if ingested. There is a certain amount of controversy about the safety of some of the products which are commonly used. It is difficult to determine what might be causing unseen internal damage and there are people who swear that lawn chemicals gave their dogs cancer.
Also consider that your public park, RV park, or athletic field may be treated with pesticides known to be toxic to your dog.