I don't think there's any chance they overturn Lawrence, which certainly Kavanaugh, certainly Roberts, probably Gorsuch, and probably Barrett would all sustain. I think the odds that they overturn Obergefell are, like, 10%, but that seems more real for a number of reasons. There are plenty of ways to read the Constitution which imply the decision in Lawrence, but I think Obergefell (and for that matter Roe) are much more blatantly made up.
I suppose I could be wrong, but I just don't think the Court wants to reopen those issues. There's a lot I think this Court wants to go after, but I think they'll just avoid the issue.
I'm more confused as to how you think Lawrence is perfectly sound while Obergefell is not. If there's one major issue I have with Obergefell, it's that it didn't have a more solid foundation in the Equal Protection Clause itself as opposed to relying more on the Due Process Clause. Do you share Justice O'Connor's view in her concurrence in Lawrence?
Basically, yes; I also think there's a general shift towards the Court interpreting privacy rights in a more broad way that's taken place in the 2010s, such that it's really difficult for me to see
Lawrence overturned.
By contrast, the thing with
Obergefell is that no conservatives really think it was decided correctly and it's protected entirely by a lack of desire to rehear the matter or reopen the controversy. Given the Senate makeup the judiciary is broadly continuing to get more conservative over time, and while I think
Obergefell is fine with the current Court I really don't know how it might fare in a court that's 7-2 or 8-1 conservative.