There are some dangers to dogs eating a cat's faeces, if the cat had parasites it may be subclinical for the cat but dangerous for the dog,
a faecal floatation test would indicate any infection.
Lungworm infections are uncommon and may not be normally considered in the differential diagnosis, but may occur; diagnosis with
faecal floatation or a bronchial mucus smear are diagnostic methods of choice, x-rays and bronchoscopy are also useful but you should discuss with your Veterinarian.