Ed's got a really great post on constitutional interpretation. Like Brayton, I think most charges of judicial activism are bunk, so much so that the word has become practically ruined by demagogues. However, that doesn't mean that the Supreme Court doesn't get it wrong, by any objective measure. They certainly do in many cases. Call it judicial activism, call it what you will, the Supreme Court has often gotten it wrong (and this was one of the key points in Randy Barnett's book, Restoring the Lost Constitution, that Brayton discusses).
For instance, the Slaughterhouse cases got it wrong. Justice Bork in asserting that the "privileges or immunities clause" was an "inkblot" and hence could be cut out of the Constitution got it wrong.
Any decision that tries to read things out of the text of the Constitution is wrong. The problem for conservatives who argue "activism" is that many decisions in which they would disagree are in no way inconsistent with the text of the Constitution.
For instance, the Constitution clearly has a textual free speech norm. And the text of the Constitution doesn't distinguish between "pornographic" videos on the one hand and videos of lunatic-wing-nuts distorting the philosophical origins of the Constitution on the other. They are both moving pictures with words and sounds. And if moving pictures with words and sounds qualify as "speech," then they are both "speech," which the Constitution's text explicitly protects.
Regarding the textual authority for Lawrence, it's the "privileges or immunities" clause of the 14th Amendment which clearly contains a substantive right to "liberty." Indeed, the Declaration of Independence states that governments are instituted among men to secure our unalienable right to liberty.
In terms of the Constitution not specifying a "right" to "sodomy" the Constitution neither specifies a "right" to interracial marriage (Loving). You will no more find that in the text of the Constitution, than you will a "right" to sodomy.
Now it could be argued Loving involves "race" discrimination and that's clearly outlawed by the Constitution. Not necessarily: Where does the 14th Amendment use the word "race"? (You can see how this, "read the Constitution so narrowly" so that if a word doesn't appear, then there can be no right...is a deeply flawed method of argument).
In confronting particular constitutional questions, we must abstract general principles from the text and the historical meaning of the Constitution, and then apply the specific set of facts to whichever particular general norm is in question.* One could seriously argue that even though the word "race" isn't mentioned in the Constitution, looking at the context in which the 14th Amendment was ratified, it clearly intended to guarantee some sort of race equality. Okay. I'll concede that. But couldn't we also concede that looking at the context in which the Declaration, the Constitution, and the 14th Amendment were passed that our framers likewise intended to guarantee a substantive norm of liberty?
The likely retort; "yes -- there is a substantive norm of liberty -- but to a point." But the exact argument could be made with respect to the 14th Amendment and race: "yes, there is a substantive norm of racial equality, found within the 14th Amendment, but to a point."
So why should that "point" on liberty be drawn so as not to include "sodomy"? Brayton gives a good and fair summary of the argument:
[A]t the time of the ratification of the Constitution, laws against homosexual sodomy were widespread in the states and were part of a very longstanding tradition of such prohibitions in Western law. Neither the founding fathers nor the citizens who ratified the Constitution that they wrote would conceive of the sphere of individual rights that they sought to protect as including a right to homosexual sodomy. Therefore, for a court to "discover" such a right in a document that they wrote and ratified is to substitute their own ideological preferences for the clear meaning of the Constitution when viewed in historical context.
But guess what, the same argument can be made in the race context. First Brown, and then Loving. Arguably when the 14th Amendment was ratified, it was not intended to be so encompassing as to outlaw segregated schools. In other words, the Framers did not know that they making segregation illegal. Now "originalists" differ on this issue. Some originalists, like Lino Graglia and Raul Berger, concede that Brown was wrongly decided precisely because the ratifiers didn't intend it to outlaw segregation. Others like Bork make a case (Bork's case is rather weak, Posner demolishes it here) that Brown was consistent with original intent. So does Michael McConnell (I've not read his case).
But whereas we can argue over Brown, we cannot argue over Loving. The 14th Amendment was ratified upon the explicit, overt guarantees and reliance that this Amendment would not outlaw interracial marriages. Not only did they not know that they were outlawing interracial marriages, they specifically relied upon the fact that the legality of miscegenation bans would be preserved.
Thus, if that's your standard, there is no way to distinguish between the Lawrence decision and the Loving decision. Saying that a specific right to "sodomy" isn't found in the text of the Constitution won't do it, because neither is a specific right to "interracial marriage" found in the text. Simply invoking the word "race" won't do it either, because we can just as easily invoke the word "liberty."
* i.e., Apply the specific fact of interracial bans to the general norm of race-equality which we extract from the "equal protection" or the "privileges or immunities" clause of the 14th Amendment. Technically, this process is known as constitutional construction, as opposed to interpretation.