Absolutely. They will send the firm a letter and ask for a response. You will receive a copy of their response. Then you should respond to it to the state bar. Dispute every lie and ask that they investigate internally. Offer the names of any witnesses who might have knowledge of the deceitful actions. Hopefully, the state bar will follow up. You should check with them to be sure they are doing something.
If they are found to be guilty, their license could be suspended or revoked. If it is a first offense, it would likely be suspended for perhaps, 3 months, 6 months or a year and they could be fined as well.
Lastly, you should demand the name and phone number of their insurance company and file a claim, that is if they screwed up your case and prevented you from going forward with it, like taking your money and missing the statute of limitations, for example. If they refuse, see another attorney and get them to write a letter demanding to know their insurance company and its phone number. It often takes a law firm to get behind such demands before places give it up. By law they have to but, you sometimes have to fight for your rights.
You have to be smart to get through law school and pass the bar in any case. For international law, you have to be aware of the laws of other countries as well.
My twin was going to do that kind of work. She became fluent in another language and was going to study abroad for a year. (Unfortunately she died during that year.)
So undergrad, you need to learn a lot about other cultures - their language and their lives. Study cultural anthropology, languages, and international relations. Knowing mediation also helps.
You might go to the hiring site for the US UN team and find out what they look for in a lawyer. It's not just the law, a lot of it is understanding their culture and point of view and being something of a diplomat.