An alternative interpretation would be to instead equate Brown with Romer v. Evans, in that both of those decisions addressed, directly or indirectly, discrimination in the areas of education, employment, housing, etc.
Along those lines, Lawrence can be compared to the 1967 case of Loving v. Virginia, which established a constitutional right to interracial marriage, because they both involve sexual relationships.
Discrimination issues faced by LGBT people are, to some extent, similar to those that affect African Americans. But there are definite differences.
Most state sodomy laws (although not the Texas statute that was directly at issue in Lawrence) prohibited activities that could be engaged in by either same-sex or opposite-sex partners. But they prohibited all homosexual activity, and only some heterosexual activity.
Therefore, those laws had a symbolic meaning that went beyond their specific prohibitions (which were rarely enforced, anyway). The broader message was that it's wrong for us to be who we are. That attitude has been gradually disappearing from American society in recent decades. But, by repudiating that notion in a legal context, Lawrence constituted a major step toward full acceptance of LGBT people in society.
For African Americans, segregated schools, the issue directly addressed by Brown, was one of the most visible symbols of discrimination. LGBT people face issues in the educational realm, but the sodomy laws were more of a central issue for us.
Lawrence is also our Brown in the sense that it does not mark the end of the struggle. There is more that needs to be done, but no one should discount the great progress that has been made, because of the results of referenda on same-sex marriage. In opinion polls, the younger age cohorts support LGBT rights more strongly than the older ones. Therefore, it seems inevitable that the remaining battles, including marriage, will be won eventually. Some of us who are already a bit advanced in age might want to quote from Rev. Martin Luther King Jr.'s final public speech:
I may not get there with you. But I want you to know tonight, that we, as a people, will get to the promised land!