Cat, Dog and Vegetables?

Our cat started chewing on our indoor house plants. She's 2.5 years 15 pound 2 ft long (nose to butt) cat.

So I started slicing up lettuce portions into her food. About half a leaf of lettuce daily. If she doesn't get her lettuce or I forgot, she would twirl around my feet to harass me. Sometimes she gets impatient that she smelled the lettuce I am cutting up for her, and she puts her front paws on the table to observe me slicing the lettuce. She eats up the lettuce in no time. She would not eat more than half a leaf a day.

We lived on a farm for a few months and our dog (pointer mutt) then learned from the horses and started chewing and eating grass. But he does not have the teeth to chew up the grass and he would regurgitate it. To prevent him from desiring for grass I too give him half a leaf of lettuce daily. He does not like eating carrots but he loves carrot soup mixed into his dog food. But so far, I have not given him carrot soup because I am not sure if carrot soup is good for him, but he never had any bowel problem after having carrot soup.

Should I continue feeding our dog carrot soup?

Does your dog or your cat like lettuce?

Do most cats or dogs like lettuce?

What do you think of the dietary behaviour of my cat and dog? Abnormal?