By default, there already is a barrel that's lying on its side/standing.
Anyway, you need to make several versions of the doodad/destructible.
One where it is standing (regular version), and one where you change the value "Art - Max Roll Angle".
By shift-clicking "Art - Max Roll Angle", you can set it to something negative. Set it to -89.6 to make it lie down.
Note that not all models have a bottom side, so when you change that roll angle, parts of the model might be missing.