"Judges should refuse to accept an appointment of Chief Justice or refuse to recognise any person appointed," the Lawyers' Collective said in its appeal.
They said such an appointment would be contrary to the Constitution as the highest court had ruled that the select committee which found 54-year-old Bandarnayake guilty of corruption was illegal.
Any replacement for the current Chief Justice would be a "usurper", the lawyers said in their letter addressed to judges.
The move to impeach Bandaranayake has come in for condemnation as an attack on the independence of the judiciary.
The select committee, which conducted an ex parte trial, found the Chief Justice guilty on three of the 14 charges of financial, professional and personal misconduct filed against her.
However, the findings were quashed by courts on Monday.
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Parliament said it will not accept the court interpretations. It will vote today to formalise Bandarnayake's impeachment and her imminent removal from office.
Meanwhile, the lawyers continued their strike for the second straight day in protest against the impeachment.