C++ Locking stream operators with mutex

I need to lock stdout in my logging application to prevent string interleaving in multi-thread applications logging to stdout. Can't figure out how to use move constructor or std::move or sth else to move unique_lock to another object.

I created objects for setting configs and encapsulation and figured out how to lock stdout with static std::mutex to lock from these objects (called shards).

Something like this works for me:

l->log(1, "Test message 1");

While that is fine and could be implemented with templates and variable number of parameters I would like to approach more stream-like possibilities. I am looking for something like this:

*l << "Module id: " << 42 << "value: " << 42 << std::endl;

I dont want to force users to precompute string with concatenation and to_string(42) I just want to find a way to lock stdout.

My approach so far was to create operator << and another object locked stream, as was suggested in other answers. Things is I can't figure how to move mutex to another object. My code:

locked_stream& shard::operator<<(int num)
{
    static std::mutex _out_mutex;
    std::unique_lock<std::mutex> lock(_out_mutex);
    //std::lock_guard<std::mutex> lock (_out_mutex);
    std::cout << std::to_string(num) << "(s)";
    locked_stream s;
    return s;
}

After outputting input to std::cout I woould like to move lock into object stream.