(This also assumes you're able to contact the person who sent the e-mail.)
Do you mean obligatory? If you really mean conditional, could you elaborate why?
So: B would be obligatory, given A.
That said, I only mentioned payment in the case where the anonymous sender seemed to be helpful, in that they provided the way the server was infiltrated (presumably in an effort to allow it to be fixed). I didn't mention how much money to offer, or what to do at all in the case where it appears to be the beginning of a shakedown, other than to note that it's naive to assume you can rid yourself of them by just dealing with the one server referenced.
Edit: Ah, found the LastPass submission. Definitely sarcasm. ;)
If this comes to ransom, rather than unethical/unexperienced gray hat thing, are there any good steps to take? Or hiring an expert consultancy is probably the only good option here?
I assume a professional computer security firm could help, but I don't know enough about the incentives at play to know whether that's good in practice (if they often deal with situations like this and not just hardening/forensics, I assume they would have good advice). I have no idea what that costs, and whether your business can afford it.
By sending just the proof he forces you to reconsider your approach to security and start from clean state.
I'm not saying you should or shouldn't, but several comments have suggested contacting this person; it's not clear that that's even possible.
Or dd if=/dev/urandom of=/dev/sda1 bs=8M
"Thank you for bringing this problem to our attention! We are taking steps to resolve the problem now, but would like to reward you for your work. If you let us know how you would like to receive if, we would be happy to donate $X to your efforts."
Where $X is something you think you can easily part with, $100, $250, $500, $1000? This both primes the sender to be more generous, if they were on the fence as to whether to do something nefarious, and establishes some small trail to them (depending on method) in case of major problems with them later.
If the proof was not included in the email, I think it's much more likely you just received the opening email in a blackmail campaign. It's highly unlikely that server is even the entry point in that case, so cleaning it will not resolve the problem. It's just the sacrificial lamb for them to prove they've got leverage and let you stew, and they can contact you again after you think you've cleaned out the problem to let you know they still have access, and the only way to be rid of them is the pay them.