I take it your friend's first referral was in the NHS?
Your friend could of course simply ask the GP a for a second opinion, which could be a private one.
But, reading between the lines, it sounds as if your friend was not happy with the GP either. If so, then they will need to tread carefully. If they're not prepared to go back to the the same GP then they could try another doctor in the same practice.
They could also try calling every private hospital in the phone book and ask if they have a dermatologist who sees patients without a GP referral but that is somewhat hit and miss.
Lichen planus is a common condition so all dermatologists should be familiar with it.