In a normally aspirated engine, when you twist the throttle...... you see an instantaneous response from the engine..... there is no lag...... whereas when you turbo charge the same engine .... the gap between twist of the throttle and the power delivery is widen. The higher the RPM the narrower the gap will become but it will always be there. THERE IS NO REPLACEMENT FOR DISPLACEMENT
There are many factors which can effect the turbo lag..... Engine RPM is just one of the variables.
Supercharger has no lag but it has its own troubles........ Its coupled to the engine crankshaft in similar fashion as the CAR AC....... what happens when u switch it ON....... gari bhaari hojati hai. Just like the Air conditioner compressor the super charger turns into a load at the beginning (lower RPM)...... as the engine goes faster the supercharger starts to make more power than its consuming and therefore makes more power as the engine goes faster.
Its always a trade-off between acceleration and top speed..... even the most highly tuned sequential twin turbo setups will have a lag.