Re: tubo lag
Turbo lag is not to be confused with turbo spool up delay.
The question is a bit open, if not truly ambiguous.
All turbocharged cars will suffer from a degree of lag. Whether this is noticeable or significant is another matter. It's also very subjective, depending upon the driver's expectations.
Car makers have got turbocharging down to a very fine art (fine science, perhaps) nowadays.
Remapping will never alter turbo lag or spool up time directly, both are by-products of the way that turbo-supercharged engines work, but tuning can provide work arounds of sorts to make it less intrusive.
Some people drive turbocharged cars almost expecting to find lag and latency. When it [turbo lag] is not there in obviously discernible measures it can give the impression to the driver that the car is not a lively as it actually is.
A crudely turbocharged car such as a mid-1980s Montego Turbo leaves you in no doubt that it is turbocharged. Is this a good thing?
Well, yes, subjectively speaking, if you really need reminding that your car is turbocharged.
Personally, I prefer the imperceptible build in torque delivery from idle speed which is the trademark of modern turbo-supercharging.
NB - turbochargers are a subset of superchargers - the turbo bit of the word simply tells us that the compressor is exhaust driven rather than being directly mechanically driven.