What is Turbo Lag?
Turbo lag occurs when a high-output turbocharger can't boost the power of an engine enough at a low RPM, which doesn't have enough exhaust flow to power the turbo fans. The turbo "kicks in" (the lag is overcome) when the RPM is high enough to get proper exhaust flow levels, which adds to the amount of air flowing into the combustion chamber, which leads to more exhast flow, getting the turbo up to full speed.
How Turbo Size Affects Lag
Small turbos (which typically don't provide as much power) are much less likely to lag because the exhaust is being forced into the turbine in a small area, so it immediately affects the turbine impeller, which immediately draws in more air into the intake.