The “general" rule here is Rule 5.4 of the ABA model rules [0], though the actual rules in a particular jurisdiction (state) may be different since the model rules are not the actual rules of any State. Note that this doesn't actually prohibit any particular structure (well, implicitly it prohibits publicly traded corporations), it just prohibits non-lawyers from being stockholders (if a corp) or partners in a law firm or (except as part of an employee compensation within a law firm) having a claim on revenue generated by lawyers through the practice of law.

[0] https://www.americanbar.org/groups/professional_responsibili...