Would you lie about having covid just to avoid seeing someone?

No.
And that is as crappy a lie as they come if that person is in any way involved with your life (and if they aren't then why speak at all). Word of contagion tends to spread like wildfire, and you'd be forced to remain in quarantine for days or likely face the consequences of violating it. It's one use only. If you do become sick in so many months the ruse will be revealed.