How to unlock a roll top desk without the key

Locksmith to open it.

Check with some key shops if they have a key for it

I'd agree with Fr-Chuck. Another option would be to contact the manufacturer of the desk, they likley use the same key and lock for many years. Desk locks are not very strong or expensive to replace. If you have no luck with the locksmith or manuufacturer you can probably drill out the lock and install a replacement for about $10