The lies on the other side only seem worse--there is no way to prove they are worse. They seem worse because they reflect values that you don't happen to agree with, and that you think are much less important than the values you hold.
If you defend the lies of your side by claiming the other side's lies are worse, does that help bring us any closer to the solutions for our problems? It's usually a bunch of useless, water-under-the-bridge blaming and name-calling.
Instead of countering one lie with a "worse one from the other side," talk about the truth--the truth of the situation and possible ways forward. Don't dwell on the past and lies. Don't defend lies, call them out as lies, then move into positive territory.