Here are the laws for my city (Saratoga Springs, UT). I'd bet most municipalities of any size have similar laws on the books. Letting their dog poop on your lawn is a violation of at least 3 sub-sections...

9.01.05. Dogs Running at Large Prohibited.
1. It shall be unlawful for the owner or keeper of any dog to permit such dog to run at large.
2. It shall be unlawful for the owner of a dog to permit such dog to go upon the private
property of any person without the permission of the owner or person entitled to
possession of such private property whether the dog is on or off a leash.

9.01.08. Trespassing Animals and Fowl.
It shall be unlawful for any owner or caretaker of any domestic fowl or animal to permit such
fowl or animal to trespass upon the premises of another. A violation of this provision shall be
separate and in addition to any other violation set forth in this Chapter.

9.01.15. Dogs Which Disturb Neighborhood.
1. No person shall own, keep, or harbor any dog which by loud, continued, or frequent
barking, howling, yelping, or by noxious or offensive odors shall annoy, disturb, or
endanger the health or welfare of any person or neighborhood.
2. A violation of this Section shall be a Class B misdemeanor and such is hereby declared a
public nuisance, and each day the violation is permitted to exist or continue shall
constitute a separate offense

The penalty is described here. Basically, they can revoke the dog's registration and be impounded:

9.01.18. Public Nuisance.
The introduction, possession, or maintenance of any animal, or the allowing of an animal to be in
contravention of this Chapter is, in addition to being a misdemeanor, hereby declared to be a
public nuisance. A peace officer, the Animal Control Officer, or their designee are hereby
authorized, directed, and empowered to summarily abate any such nuisance by any means
reasonably necessary, including the destruction of the animal or animals involved.
(Ord. 11-9; Ord. 07-4)
9.01.19. Revocation of License.
If the owner of any dog is convicted of a violation of this Title on two or more different
occasions during any consecutive twelve month period involving the same dog, the license of the
dog involved shall be revoked. The animal control officer or authorized police officer shall
immediately impound and pick up any dog whose license has been revoked. Any dog impounded
following revocation of its license shall be dealt with in accordance with the provisions of City
ordinances for impounded animals except that under no conditions shall the animal be allowed
back into the City.

https://www.saratogasprings-ut.gov/DocumentCenter/View/531/Title-9---Animals?bidId=