To my best knowledge, the framework does not provide such capability. It is quite possible that you can implement it if you dive into NDK, but I don't know the details.
I can think of one very complex scheme involving AIDL and Binder counting, but it is more like a theoretical approach and I wouldn't use it myself (because there is no way to reliably test locking scheme).
I know of two workarounds for this task: file locking and socket locking.
File locking is described here in details.
As far as I know, file locking allows you to lock across processes, but not across threads in the same process. This means that you need to make sure that you don't rely on this mechanism for intra-process multithreading.
Socket locking is described here. I have never used it myself though.