For a raw LV, you'll probably have to use "dd" to copy it, and yes, it will be necessary to shutdown Oracle.
1) Create an LV on the new VG (it will have to be named different) of the exact same size.
2) Shutdown Oracle
3) dd if=/dev/rsourcelv of=/dev/rdestlv
dd takes a variety of flags for block size and count. You will probably want to experiment with these to determine which performs best for you.
* You *can* perform speed testing with this with Oracle up to determine a reasonable block size, just remember that the destination will be trash, until you do it with Oracle down.
4) Rename the original LV to a new name
5) Rename the new LV to the original's name
Now at this step, I *believe* Oracle should be fine. You have the ability to put the original LV in place if you need to, assuming Oracle doesn't mess itself up (which I have known it to do when using files instead of raws).
And as always, backup first! You can never have too many backups.