Simply putting what he just said, Barrel cannot be chained to the effect of paying life points.
You can not chain it to Solemn Judgment's pay cost, you can not chain it to Imperial Order's pay cost, you can not chain it to Mirror Wall's pay cost, you can not chain it to CED's pay cost (but to CED's effect itself you can).
You can only counter effects that deal direct damage to your LP, and most that say so include the words "inflict" in their effects. Barrel Behind the Door was most commonly used with a combo with Ring of Destruction. Say you activate Ring on their Dark Ruler Ha Des, and ask if they wish to respond, if they do not, you can then chain your Barrel to Ring and they would end up taking your end of the Ring as well, so they end taking 2450 X 2 = 4900 directly from your combo there.
Remember, that Barrel cannot be chained to another Barrel, Barrel Behind the Door is simply redirecting the damage, it is not dealing the damage itself, the initial card in the chain is doing that.