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It does with this engine, 1-3 and 4-6 have separate exhaust manifolds, precats and O2 sensors.

There is a couple of scenarios that could relate to your problem with starting. The issue of the temprature sensor for cold starting,as raised its head a few times on the Ls400 engine .There is a sensor located just to the left of the front of the engine below the second bank coil.it should be green in colour and screws into the head to the side of the water pump, this is the cold start temprature sensor .The purpose of this sensor is to guage the temprature of the coolant and on that information sends a signal to the engine ecu instructing it to increase or decrease fuel in the combustion mixture. It as a double edged affect depending on how it fails and because the other effect is too much fuel even after the engine as warmed up it is difficult to ascertain weather that is the cause of poor starting . They are not expensive and worth a punt just to eliminate that as a cause of the problem. The other scenario that occurs is the stop too soon after start and that occurs even on my 25k engine if you stop the engine a few seconds after start up .What happens is the plugs get saturated because the ecu on information from the coolant temprature sensor is instructing the fuel injectors to flood the chambers with extra fuel and when simultaneuos ignition occurs the engine starts normally the problem then occurs because the plugs will be wet and won't dry out if you immediatly turn off the engine when an attempt is then made to restart the more the engine is cranked the more saturated they become .The reason this does not happen when the engine is warm is the fuel evaporates immediatly it enters the chamber either by heat or combustion.That is why it starts after a rest period.That might not be your issue but it is an issue on cold engines and not just Lexus engines.