
It's increasingly common to blame the growth of population in foxes for every ailment known to canine kind - in certain cases yes, their increased presence has a bearing but they're not responsible for a fraction of what they're blamed for :)
Lung worm is commonly passed on by dog faeces and the common garden slug/snail. Dogs eating either of these or chewing on toys or bones or sticks or plastic bottles whatever else is around overnight in a garden or park that may have been in contact with slugs or snails are classic ways of lung worm being picked up - for the average pet dog the risks are therefore fairly high, particularly since our damp summer months through autumn were an ideal breeding ground for increased snail population nationwide.
Lung worm is treatable, usually by around 10 days of panacure granules or similar - routine worming may, but wont necessarily,
prevent lung worm but it wont
cure it if already present. It has to be treated separately. If untreated lungworm can be fatal.
I can't possibly say if your dog has lungworm and presumably your vet thinks it unlikely since you've raised the issue and not been provided with meds to ensure it's killed off however it is better to know the facts of the disease rather than assume that if a dog hasn't eaten fox or squirrel poo it can't be infected....
ETA>Can lungworm manifest itself 3 months later? I have a feeling that the answer could be yes.
Yes, as with any parasite left untreated, it multiplies and symptoms will vary dog to dog both in how rapidly they appear and how serious the signs.