Hello, my name is***** and I have over 20 years of experience as a veterinarian. I'm sorry to hear that your pup Lucy ate something she should not have.
The ball pieces may pass if she chewed it into small enough pieces but if she just ate it, within the past 2-3 hours, it's worth trying to get her to vomit it back up.
You can give her 1 tablespoon of 3% hydrogen peroxide per 10 pounds of body weight mixed with bread chunks or ice cream (no more than 3 tablespoons even if she weighs more than 35 pounds).
Then take her outside and run her around to get the peroxide bubbling so she vomits.
If no vomiting in 10 minutes repeat the peroxide dose once.
If she vomits and seems to clear her stomach and be done I would check to see if the pieces are present.
Once she finishes vomiting and empties her stomach to try and settle her stomach today you can give either:
1) Pepcid-ac (famotidine) at a dose of one half of a 10mg tablet per 10 to 20 pounds of body weight every 12 hours.
2) Prilosec (omeprazole) at a dose of one half of a 10mg tablet per 10 to 20 pounds of body weight every 24 hours.
These will reduce stomach acid and should help settle her stomach after she's cleared her stomach.
Then feed a homemade diet of 1/3 boiled, lean hamburger or boiled, white, skinless chicken, all fats and juices drained off the meat, and 2/3 boiled, plain, white rice. Add 2 tablespoons of canned pumpkin, (not pie filling, just pumpkin), to each meal for fiber whether she vomits most of the ball pieces back up or not to help push the remaining pieces through.
If you don't have peroxide you can get her to an emergency clinic to induce vomiting.
If she doesn't vomit it back up or you choose not to take her to an emergency clinic still use the bland diet with pumpkin to try and get the pieces to pass.
If it has been several hours since she ate the ball it is likely too late to induce vomiting, the pieces will likely be out of her stomach. All you can do at that point is watch her closely. If she starts vomiting, has a tense painful belly or refuses to eat or runs a fever (more than 103F rectally) then that can signify a blockage and she should be seen by a veterinarian immediately. Surgery may be needed at that point.
Please let me know if you have any further questions.