Turbo lag is a physical function of the engine design and is inherent. It does NOT go away magically after some period of time or mileage. If you experience another similar characteristic that DOES go away after some time or mileage, then it is/was DEFINITELY NOT turbo lag. Designers and manufacturers work hard to balance turbo lag with the acceptable driveability that it brings (or not). It becomes a matter of cost versus gain in making good power, achieving good fuel economy and then providing good driveability. Turbo lag has been around since turbos were first used to improve internal combustion efficiency. There are many incremental techniques used to reduce its negative effects whilst maintaining better power from smaller displacement engines and managing good - acceptable, driveability.
Driveability btw, includes the comparative feel of the turbocharged engine with one that isn't, along with the gains in power and fuel economy. Turbo lag is by definition an almost necessary fault of even having a turbocharger. Sequential smaller turbos can reduce this effect to almost imperceptible, but do NOT even imagine it's not there. It is. About the only way to completely eliminate it is to physically decouple the turbocharger from the exhaust that drives it.
Think about it this way : the turbocharger must first receive exhaust to spin, THEN it can provide compression or boost of inlet mixture to the engine. The exhaust gas has to have been first taken in, so lag is the time it takes for the first inlet air to be combusted, before it can then be sent to the turbocharger to then compress second new air to gain power (and feel of acceleration). This just cannot be avoided - except by :
...an Audi innovation now under development, that's uses not exhaust gases, but electric motors to spin the compressors before they can be turbochargers. The first charge of air is compressed by electricity, then when it becomes exhaust, it can then spin the turbocharger becoming a better efficient design (than the electric motor) while at the same time COMPLETELY eliminating turbo lag, cuz the electric motors are always at the ready to provide boost when there isn't enough exhaust first.
The prototype works great - 600 hp out of a 2.5 liter 5 cylinder (yes the very same derivative from the Ur Quattro, and later TTRS and RSQ3) this car is now in development and has proven to hold improved rotational dynamics that allow it to spool up to full power MUCH faster than a sequentially turbocharged same displacement engine (with the same peak power). That means quicker acceleration in time to distance metrics - all while improving fuel efficiency (and of course fuel economy too)...