Is it lying or is it acting 🎭 Shakespeare does say all the world is your stage

Neither. He actually says something else, and it's a metaphor - neither acting nor lying:
All the world’s a stage,
And all the men and women merely players;
They have their exits and their entrances;
And one man in his time plays many parts,
His acts being seven ages. At first the infant
Mewling and puking in the nurse’s arms;
And then the whining school-boy, with his satchel
And shining morning face, creeping like snail
Unwillingly to school. And then the lover...

Tomorrow, and tomorrow, and tomorrow,
Creeps in this petty pace from day to day,
To the last syllable of recorded time;
And all our yesterdays have lighted fools
The way to dusty death. Out, out, brief candle!
Life's but a walking shadow, a poor player,
That struts and frets his hour upon the stage,
And then is heard no more. It is a tale
Told by an idiot, full of sound and fury,
Signifying nothing.

Did he say that?

Hmmm...?

Anyway its acting out...and acting out is pretending, where pretending could be a lie

The suspension of Disbelief.

It’s about more than literal acting; a metaphor for the course of a lifetime.