I have a 30 year old donkey in with four horses. I will say, two vets have mentioned the possibility of lungworm to me, but they thought since she's been here with no problems for anyone for three years that we were in the clear. Sorry I can't really be of more help!
We've had a donky for 25 years- she's always been out with the horses and we've never had issues. All are on a rotational deworming schedule (depending on FEC's, season, total number of animals, etc.). I would check with your vet and see what they think. Our vet also pastures her horses with a donkey, so I don't think she's too concerned!
If you are in love with the donkey then call your vet and run these concerns by him or her. Then I would suggest setting aside an isolation area for the donkey to stay in until you can have the vet check the donkey and run a fecal exam. Deworm the donkey according to his/her instructions in order to protect your pastures, and then put the donkey on the same worming protocol you use for your herd. That should protect everyone.
Estimates on the percentage of donkeys infected with range from 4 percent to 70 percent depending on the place the studies and estimates have been done. My donkey came from a zoo with good health care in place. I did what I outlined above, and all went well. A physical exam and a vet approved worming program will take care of the problem and keep your herd safe.
I intended to insist that the foal has a zero fecal count for lungworms before I will buy her. If she needs to be treated I will pay a deposit but I won't take her until she test free.
I asked the breeder today about lungworm and she dismissed it as a myth (we have had donkeys and horses for X years with no problems...bla bla bla) which tells me she has never checked for it. Lungworm is not normally what the vets here look for in fecal tests.