As I have heard the term used, a "lawyer's lawyer" is a lawyer whom the top members of the bar see as a top member of the bar. If that's the definition, then I agree with Adam about John Roberts. Roberts was not only a lawyer's lawyer, he probably was the lawyer's lawyer of the Supreme Court bar of his generation. I clerked for Justice Kennedy in OT2003, and Roberts was already a legend as an advocate. People used to say that Waxman and Clement were good, but too bad you missed John Roberts (who by then was already on the D.C. Circuit). According to rumors circulating among the Supreme Court bar, the justices of the Rehnquist Court generally saw him as the finest advocate of his generation.
My sense is that Diane's definition is different. Diane, please correct me if I'm wrong, but my sense is that you see a "lawyer's lawyer" as more of a skilled legal technician who lacks a clear ideological agenda. Under that view, as I understand it, a lawyer's lawyer is someone who is interested in the law as law and is not on any particular ideological "team"—and, perhaps implicitly, would follow that law faithfully without bias if confirmed as a judge. I tend to agree with you that this lack of an agenda is part of the term "judge's judge," but I don't see as implicit in the term "lawyer's lawyer."
I don't know if either definition is necessarily correct or more common. But I wonder if the disagreement between Adam and Diane is mostly about finding the right definition of the term. Also, perhaps it's worth noting that both Roberts and Stevens pass the "lawyer's lawyer" test with flying colors under the first standard, but that there would be sharp ideological divisions today about both Roberts and Stevens under the second one.