You’re being a little too binary about this. The point isn’t that if objectivity is a myth then lies don’t exist, the statement is meant to challenge the idea that there is one side to a story. Hell in the US we basically say “there are two sides to each story,” when that isn’t true either.

Example: when did WWII start? Well, depends on who you ask. The Polish will tell you one thing, the French another, the Chinese will definitely tell you something different, because for them it began when Japan invaded Manchuria and had basically nothing to do with Germany. No one is wrong, but there isn’t one objective answer. That’s the point here. We have to consider multiple, sometimes somewhat competing narratives that still somehow don’t contradict each other. They can be acknowledged and integrated into a complex narrative. But we often want to reduce things, it’s a natural human tendency.

So whenever I see someone say something like “well Wikipedia is biased,“ well yeah, no shit. But that doesn’t mean anything. You account for the different narratives and perspectives people have, the different lenses through which they view the world, and you come to a conclusion. Going “I won’t be satisfied until I have an unbiased source” is not productive, and you would be surprised how many people act like that is the bar.

There’s a dry but still interesting work called That Noble Dream that is a pretty seminal historiographical work which covers “the objectivity question.”