3 symptoms, engine start....what's the cause?
 

check engine light on

faint smell of gas inside on warm day with windows rolled up and after car sat overnight

heavy combustion smells outside of car after initial start, at least on these very cold winter mornings.

thought culprit might be failed secondary air injection pump at exhaust...but Lexus catalog doesn't even show that item.

Have you checked to see what the check engine code is? Sounds like it might be an issue with the EVAP system leaking somewhere.