The lawyer filing the brief is not violating any ethical rule involving duty to a client unless he acts in mannner contrary to the client's best interests (or expressed wishes on some matters withing the client's sole discreation).

   The brief says the  POLICY of the DOJ is to defend lawfully encated statutes regardless of whether the current Administration supports the underlying policy. It would be quite a research project but I'd be interested in seeing if throughout history the DOJ has every single time opposed actions seeking to have a federal statute declared unconstitutional or  on its face or unenforceable in a specific application.

   I'd suggest the research might start where the USA and members of administrations  have been defendants in actions brought under various statutes and then wanted to  put forth the defense the statute is unconstitutional or can't be constitutionaly applied to them. Do DOJ lawyers always refuse to put forth such arguments? Or, do they just say hey it's bad policy to compel the President or a subordinate to do this  or forbid him to do that,  but despite the fact we believe this statute violates, for example, the separation of powers we won't argue that point because it's a duly enacted statute?

  Even if that were to be true, that policy would not have the force of law and I don't see a citation to a statute requiring defense of a statute.

    On the other hand, there is a very important distinction between believing a statute is unconstitutional and believing it is bad policy. the latter should be left to the political arena.

[article II]Section 2 - Civilian Power over Military, Cabinet, Pardon Power, Appointments

The President shall be Commander in Chief of the Army and Navy of the United States, and of the Militia of the several States, when called into the actual Service of the United States; he may require the Opinion, in writing, of the principal Officer in each of the executive Departments, upon any subject relating to the Duties of their respective Offices, and he shall have Power to Grant Reprieves and Pardons for Offenses against the United States, except in Cases of Impeachment.

He shall have Power, by and with the Advice and Consent of the Senate, to make Treaties, provided two thirds of the Senators present concur; and he shall nominate, and by and with the Advice and Consent of the Senate, shall appoint Ambassadors, other public Ministers and Consuls, Judges of the supreme Court, and all other Officers of the United States, whose Appointments are not herein otherwise provided for, and which shall be established by Law: but the Congress may by Law vest the Appointment of such inferior Officers, as they think proper, in the President alone, in the Courts of Law, or in the Heads of Departments.

The President shall have Power to fill up all Vacancies that may happen during the Recess of the Senate, by granting Commissions which shall expire at the End of their next Session.

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The DOJ and office of AG are  established by statute (cuurent 28 U.S.c. §§ 501 and 503, respectively). Other provisions in chapter 31 of the title address the representation of the interests of the USA in court, most saliently:
And, most saliently, perhaps:

§ 530D. Report on enforcement of laws

 (a) Report.--
(1) In general.-- The Attorney General shall submit to the Congress a report of any instance in which the Attorney General or any officer of the Department of Justice--
(A) establishes or implements a formal or informal policy to refrain--
(i) from enforcing, applying, or administering any provision of any Federal statute, rule, regulation, program, policy, or other law whose enforcement, application, or administration is within the responsibility of the Attorney General or such officer on the grounds that such provision is unconstitutional; or
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