It's not very elegant, but the quick and dirty solution is to use sudo to allow certain users to run specific commands with a real uid of root.  You can say exactly what arguments the user has to use - the sudoers file is where this is configured.  Or you can make a script - which is probably better.  But said script should have no arguments, or as few as possible - because any complexity allows that user to attempt to exploit it to acheive root.  Such a script could trivially bring a specific LV online, writable by a specific user.  More complex requirement would be - more complex.

If LVM has more elegant features for this kind of thing, I'm all ears.