COCA 语料库有这样的例句，即 a lie 后接同位语从句。

In all the books and manuscripts kept in Alexandria and Rome there was absolutely no reference to the wife of Jesus. So the papyrus fragment is fabricated, manipulated and concocted. Dan Brown also scandalized Jesus in his book, The Da vinci Code. Dan Brown told a lie that there was a secret code in da Vinci's painting, The Last Supper.

如果lie用定冠词限制，则更可能后接同位语从句。例如COCA例句：

Today TPTB brag that most will walk into what they know is their execution without even having to be told the lie that they are going to be de-loused.

I agree with you about the All-Star game being the pivotal point, especially when 50,000+ plus people at the park and????? millions watching on TV saw the catcher get in front of the plate and pick up Obama's bounced throw from the mound while the media told the lie that it didn't bounce.

Then Trey told the lie that all parents-to-be have to tell themselves... in order to procreate...

可以。lie 作动词时，因为不及物，所以后面习惯上不接宾语从句，尽管偶尔在英美报刊也会看到有人这样用，但这是不规范的。lie作为名词就没有这个限制了，可以接同位语从句，也可以接定语从句。请看几个出自外媒的lie引导同位语从句的例句：

1.Dan Brown told a lie that there was a secret code in da Vinci's painting.

2. Is it a lie that we love you?

3. Is it also a lie that while in captivity, you converted to Islam? 

4. The orgy of destruction that has occurred in the wake of George Floyd’s death has been justified by a lie — that the United States is irredeemably racist to the core.