It may be professional misconduct for a party’s lawyer to communicate with the judge’s associate (or, of course, the judge) without her opponent’s consent if the purpose of the communication is to influence the conduct or outcome of the case: Legal Profession Complaints Committee v NKC  WASAT 77 at  et seq. In this solicitor’s case, the disciplinary tribunal said the unilateral communication amounted to ‘a substantial failure to reach the standard of competence and diligence that a member of the public is entitled to expect from a reasonably competent Australian legal practitioner’.
Victorian solicitors’ conduct rules say at r. 18.5
‘A practitioner must not, outside an ex parte application or a hearing of which the opponent has had proper notice, communicate in the opponent’s absence with the court concerning any matter of substance in connection with current proceedings unless:
1. the court has first communicated with the practitioner in such a way as to require the practitioner to respond to the court; or
2. the opponent has consented beforehand to the practitioner communicating with the court in a specific manner notified to the opponent by the practitioner.’
I know of at least one complaint to the Legal Services Commissioner against a Victorian barrister for filing supplementary submissions after the close of argument which was found made out but not prosecuted. The appropriate response, in the event that this increasingly common wrong is perpetrated against your client is to write and request consent to a reply, and in default of an appropriately timely consent, apply for the relisting of the matter to complain in open court.
The rule was recently reiterated by the Full Federal Court in Comcare v John Holland Rail Pty Ltd (No 3)  FCA 164, albeit from the perspective of what a judge should and should not do:
‘The rule is that a judge should not receive any communication from anyone concerning a case that the judge is to decide, made with a view to influencing the conduct or outcome of the case. See, for example, Re JRL; Ex parte CJL (1986) 161 CLR 342 (“Re JRL”) at 346 (Gibbs CJ) and 350 (Mason J), both citing Kanda v Government of Malaya  AC 322 at 337 and Reg. v Magistrates’ Court at Lilydale; Ex parte Ciccone  VR 122 at 127. In this context, communications made by one party without the knowledge of the other are governed by the principle that a judge should disqualify himself from hearing a matter where a fair-minded lay observer might reasonably apprehend that the judge might not bring an impartial mind to the resolution of the issues in the case: Ebner v Official Trustee in Bankruptcy (2000) 205 CLR 337 (“Ebner”) at 344; British American Tobacco Australia Services Ltd v Laurie (2011) 273 ALR 429;  HCA 2 (“British American v Laurie”) at 464-5, -; Re JRL at 351. This is the apprehension of bias principle.’
See also R v Fisher (2009) 22 VR 343 at  to  (VSCA).