Is there a specific type of attorney?

Depends on the country. In the UK I'd probably go to the Law Society website and search for a B2B lawyer under "Business -> Dispute Resolution" or "Media IT and intellectual property" (https://solicitors.lawsociety.org.uk/). Having used lawyers like this at start up companies in the past they are not cheap. However in the first instance you'd probably just want them to send a letter on headed notepaper, which might be enough to get someone's attention at Facebook and get the matter resolved.

Is it possible to leverage another case filing, to reduce lawyer fees? Or some sort of Nola Press DIY process? Since it seems so common.

Odds are you won't need to involve any judiciary institution, just lawyers. On that case, there's no case and no filling required.

If your country has a working small-cases court system, there are good odds you can achieve the same result without any lawyer involvement at all. But if you are discovering this from a random internet comment, you are almost certainly better talking with a lawyer about it anyway.

Take Facebook to small claims court. They can't bring a lawyer, it will cost them a small fortune and they'll lose.

What exactly is the claim you would sue for?

Finding that out is why I'd consult a lawyer.