What is the English word for a lawyer's client?

Following the idea of counterparts, the appropriate pair is:

litigator / litigant

See this answer for initial reference. The following provides more detail, as I found that both terms are somewhat ambiguously defined in the standard online resources.

Litigant is defined by ODO as "A person involved in a lawsuit." Dictionary.com and Merriam-Webster offer a similar definition. Now, I'd always thought of a litigant as strictly the plaintiff, in the sense that they are the one who litigates, but it seems my reliance on the suffix -ant to denote the agent of the action (e.g. propel/propellant, defend/defendant) was misplaced.

To dispel any doubt, this source makes it clear that litigant means "plaintiff, defendant, petitioner, respondent, cross-complainant, and cross-defendant, but not a witness or attorney" [my emphasis].

Litigator has two meanings according to Dictionary.com (but read on to see why this can't be trusted):

1. a courtroom lawyer.
2. a litigant.

It cites the word origin as

agent noun from Latin litigare (see litigation ). Latin litigator meant "a party to a lawsuit; litigant."

Unhelpfully, it also notes that "litigator" can be confused with "litigant".

Two other sources are even less useful: ODO simply defines it as the noun derivative of "litigate", which means "Resort to legal action to settle a matter; be involved in a lawsuit", and similarly Merriam-Webster goes no further than naming it as the noun form, along with "litigation".

The Free Dictionary is equally unhelpful, defining litigator as "a person who litigates" but failing to specify whether the lawyer involved in the lawsuit is "litigating".

Thankfully, however, the same site has a "legal" tab. This definition, citing Burton's Legal Thesaurus, is quite explicit:

litigator noun
appointed counsel, attorney, counsel, counsel representing a party, lead counnel, legal adversary, legal opponent, litigating attorney, littgation counsel, of counsel, opposing counsel, retained counsel

TL;DR: On the basis of all the above, I think I can confidently declare that a litigator is a lawyer, and the counterpart - the litigant - is their client.