This is a fairly general answer, as much of the nature of what could happen depends on what the first lawyer did or didn't do, state of Missouri laws, and rules of the Missouri State Bar.
The friend could find another lawyer so they both can determine exactly what happened with the forgotten filing by the first lawyer. Your friend will need to find a lawyer who has no conflicts of interest with the first lawyer, which could be difficult.
The first lawyer will realize they need to be truthful about what happened. The new lawyer could advise your friend if the forgotten filing was negligence, an "honest mistake" according to the lawyer, or somewhere in between, and if it might be possible to recover damages for not being part of the original suit, or for breach of contract, etc.
With that evidence, your friend, with the advice and/or help of the new lawyer, could either
1) file a ethics or disciplinary complaint with the Missouri office that disciplines lawyers for ethics and other violations Office of Chief Disciplinary Counsel.
2) sue the first lawyer for negligence, breach of fiduciary duty or for breach of contract.
Your friend could file an ethics complaint with the OCDC - and without the aid of a lawyer - with whatever information he/she already has from their work with the first forgetful lawyer. The OCDC complaint process is geared towards non-lawyers. But if your friend gets help from others (non-lawyers) with filing a complaint, check with the OCDC first as to if that is allowed and to what degree.