wearing a lie? holding up a lie
I googled and see there are people using these two verbs for the word lie. I know the usage is not common, maybe 'holding up a lie' in particular, but I would like to know what does these two phrases means? What are the differences? Or what images or meaning you are thinking of reading these two?

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I had to google both of these myself - i have never heard of "wearing a lie" - I have heard of" living a lie" - which I think what you are getting at when you say "wearing a lie" - Which "living a Lie" would also mean the same thing as "holding up a lie".

My interpretation -a  person knows the truth and continues to perpetuate the untruth.

hope that helps