No, even if the lawn treatment may be safe for dogs and cats, it won't necessarily be safe for your pet chickens. Remember, dogs and cats are not foraging the lawn like your chickens are. Even if they nibble on a piece of grass, your lawn is just not going to be a large part of your dogs' or cats' diet!
If you're doing a pelleted treatment, your chickens may be foraging those pellets out of there! And if it's a sprayed treatment, they could be eating whatever has been sprayed on. Sometimes lawn treatments include things like weed-specific herbicides, pesticides, pre-emergents and more. You don't want your chickens eating that stuff, and you don't want them passing it along to you in their eggs.
Here's the thing: Your chickens will scratch your lawn up, wallow holes to dust bathe, and poop their own fertilizer out onto your lawn.
They'll eat weeds--hooray! And then they'll spread weed seeds around in their droppings. If you have chickens, you are just not going to have a manicured, perfect lawn. Not even if you could apply all your treatments.
Now, you may be able to have manicured areas if you fence your chickens out of those areas, and take other steps to combine chickens and gardening or landscaping. There are ways to keep your chickens from scattering your mulch, and you can plant herbs and other things that chickens won't eat to the nubs like leafy potato chips. And with care (making sure the treatment won't blow or spread to the chickens' area), you might be able to have parts of your lawn treated so long as they're not areas the chickens have access to. Have chickens in your backyard? You can probably still have your front yard treated without issue
But is that really what you want to do?
Instead, consider weeding the lawn with old-fashioned elbow grease. Or enjoy the dandelions and violets and clover, which provide food for bees.
There are worse things, after all. You COULD be living in a town that doesn't allow chickens, and that would be a real nightmare!