1. IT is absolutely not necessary for Partners /Directors to be Advocates or Lawyers to conduct business of a Law Firm. There are scores of such Law Firms, even in India. Google Search the same for your requirements.
2. However you will need to engage ONLY registered Advocates to handle the legal matters and appearances in Court /Authorities. Proper Time-Limit Indemnity Bond may be taken from such Advocates restraining them against leaking or breaking clients.