Sounds like the engine is flooding and soaking the plugs this is a common fault on lesser cars but usually unheard of in a Lexus.The fuel is poured in on a cold start and if the engine is allowed to get to a running temprature mode any excess fuel quiclkly evaporates before it soaks the plugs.If the engine is continually using the cold start mode which is controlled via the ECU from a temprature sensor in the engine coolant it will excaberate the problem, because it will continue to soak the plugs ,hence the strong smell of petrol .If you are not getting any problems with normal starting after the engine as been running for a couple of minutes then the foregoing will probably be the answer to your problem.If the problem starts to become frequent there is a fuel management fault get the engine fault code system checked for any held code malfunctions.