While it's a feature most often abused than used as morally forgiven last minute cancellation due to real life emergencies, it's not enough of a reason to deny the tool from those who actually cannot resume the game.
I wouldn't say costing them LP because that might target who we don't want to punish, and that doesn't do anything in normals or aram/featured. Something reasonable would be little to no consequence for the first dodge, but if you dodge 2nd time on the same day, you can't queue for the next 24 hours.
If you think this is harsh, you simply aren't aware that 99.9% of the dodges are abused rather than morally accepted reasons and, well, if you're in the situation where you have to dodge twice on the same day, chances are, you probably shouldn't be playing until you sort your life out. If you think this is too light, just take into consideration that this might hit those who aren't actually abusing it and we can't make it too severe.