First, it’s important to qualify verbiage. Startup attorneys usually don’t accept equity as a ‘substitute for payment’ since that arrangement would tend to implicate a lawyer’s ethical responsibilities.
Professional responsibility (a lawyer’s legal ethical obligations) are controlled by state law. Even while they may differ among and between states, what doesn't vary is that a lawyer’s integrity and advice must always remain independent and should never be compromised.
Moreover, the ABA (American Bar Association) Model Rules - while not prohibiting this type of an arrangement - do caution that it sets the stage for a conflict of interest between a client and attorney; at some point, there could realistically arise a situation where the interests of the lawyer and client do not align. It is at this intersection that the potential for discipline begins to expand for the lawyer.
If receiving equity as some form of payment is pursued by the startup client and attorney, it’s best executed with lots of documentation and total transparency. State Bar associations invariably offer their members free guidance regarding how best to proceed with respect to these ethical dilemmas. Clients are also usually able to submit questions or receive some guidelines about these types of transactions.
As always, it’s best to seek advice from your own independent attorney.