Apologies for the delayed response. You can certainly still have a decent looking lawn without herbicides. If you are understandably still concerned, there are a number of cultural practices that can improve your lawn - even with pets using the yard.

With or without herbicides, the best way to protect your lawn against weeds is to pay close attention to your cultural practices and to be on the lookout for issues before they get out of hand. 

Cultural care- Make sure you have a robust/vigorous stand of grass in your lawn to create a competitive environment for weeds. Practices could include re-seeding areas where the grass stand is thin or has been removed, fertilizing the grass (early-spring and/or early-fall), watering when conditions are dry, and increasing your mowing height (~3.5", this last one will not help with all grassy weeds but will help with broadleaves and stress management). 

Scout for weeds- You need to be on the lookout for weeds emerging from seed. Some weeds can linger as seeds in the “seed bank” of the soil for decades! Controlling these weeds could include manual removal or smothering with a small tarp of other impermeable material temporarily if there is something very challenging (followed by replanting). 

More information on lawn care from the MSU Extension Turfgrass site: https://www.canr.msu.edu/home_gardening/lawns/

I appreciated the lawn care information, but you didn't answer my question as to the harmfulness of herbicide for dogs.

I appreciated the lawn care information, but you didn't answer my question as to the harmfulness of herbicide for dogs.

There is not necessarily a definitive answer to your question. Your veterinarian would be the professional most likely to know of any specific studies (or to know of the latest studies) related to herbicides and pets. 'Safe' is a complicated and sometimes relative term as well. 

Of course, you would want to follow any and all instructions on the herbicide labels. Pesticides and herbicides typically have a 're-entry' time where it is considered 'safe' to be in an area once a treatment has been applied. Sometimes that time period relates to how long the application it would take to dry.

If you are at all concerned about any herbicide applications impact on your pet, there is no need to have the herbicide applied to your lawn. You can certainly have a decent looking lawn without any herbicide applications by adjusting cultural practices and regular scouting for weeds.