Lawrence v Texas was not decided on some "right to privacy".
"Held: The Texas statute making it a crime for two persons of the same sex to engage in certain intimate sexual conduct violates the Due Process Clause of the Fourteenth Amendment."
Justice Anthony Kennedy wrote an opinion declaring that the liberty and privacy rights found within the Due Process Clause of the 14th Amendment to the United States Constitution confer upon consenting adults a right to engage in sodomy, and seemingly anything else they so choose, within the privacy of their homes.
Could ALL men have anal sex with ANY woman?
There was no "unequal protection". All pairs of men and all pairs of women were prohibited from engaging in same sex sodomy.
Your interpretation of "equal protection" would legitimize same sex marriage.
Also note, if it was about "equal protection" and not "right to privacy" that struck down ALL sodomy laws, what do you say to the handful of states that saw their sodomy laws (prohibiting the act between all persons, heterosexual and homosexual) ended with this ruling?