The only place where I think this could be somewhat realistic would be the Throne Room for AAR and possibly the Gameroom for games that ended or are cancelled.

Some people for instance don't want comments in their AAR (and people post regardless) and instead of getting a mod to delete someone's post (not really going to happen usually) each time it happens, having a personal lock/unlock for those topics may be useful.
Similarly, if its an announcement thread for something you made (say, a mod) where only you should be posting and it would be taking a lot more effort from the mods to open/close it for you than doing it yourself.
Lastly, upon further reflection, the watchtower might also be a place where such a function would be handy for a case closed / I understood /got my answer. People tend to hijack other people's watchtower topics at times afterall.

Other than that, there usually wouldn't be a need for a personal locking option with moderators nearby (and willing). Example: Say a debate in a SP subforum is deemed done by the OP and he closes it. People who posted there still want to post however (and legitimately so). By locking it, it would create even more duplicate discussion topics than there are already.