I thought I would post an update as we were back at the vets for a review today.
About a week after we started the steroids Lilly's nose looked like this (which was slightly better!) -

We had a further 2 weeks of steroids taking 10mg a day the I cut down to 5mg a day about 5 days ago.
She is much better and her nose is almost healed.
The vet doesn't know the exact trigger for it and even with tests we probably won't know.
We are tailing off the steroids but we might need to restart or keep her on a low dose long term.
We are happy things are much better however and will just play it by ear.
Apparently it is common in middle aged dogs....not puppies or seniors. It can affect anywhere skin joins mucous membranes....vulva and nose are most common but also eyes, gums and anal area at times.
Steroids are the mainstay of treatment.
Lilly is her usual laid back deer chasing self so all is good with us.