Actually, in the German Lexus Owners club has been explained that there is no learning mode for the driving style, but just the on-board computer logging the exact parameters of the engine to optimize performance. I only drive my Lexus, no idea what is under the hood (but I like it, hehe), but this is contradictory information. I am confused...
the information about learning mode I wrote I do not have from any technical material or from lexus. I've never ask them. It comes from my experience with my car and also I confirmed myself with other Lexus IS, which I took for a drive. (the owner has high consumption and did not believe it is possible to reach my numbers).
I did drive my style, but the results started to show up after 30 kilometers or so. On the other hand I have to say, that his car was more responsive. So I believe, that there is a learning mode, or re-calibration mode, or something like that.
Maybe this is good for the diesel, but definately not for the petrol engine
you're right, petrol engine needs different style of driving.
Never use neutral gear when driving. First of all it is dangerous, and on top of this, you will actually increase consumption when doing so. Use a long gear instead. At least that is what experts at ADAC (sort of the German AA) claim (among others) and it makes sense from a technical point of view (it has been measured too, AFAIK).
this claim is applicable for downhill driving, where it may be dangerous going on neutral (overheating brakes) and the claim with consumption is also correct (on neutral car consumps 1-2litres per hour, while going with gear without gas means 0 consumption).
However, on straight road it is not dangerous and regarding consumption - if you want to use car inertia, it is up to the situation, whether use gear or not. For longer distance is better neutral - because you won't cover it with gear in, this means you will have to press accelerator and you will certainly have higher consumption than 1-2litres per hour (the absolutly lowest consumption I can reach on straight road is about 3.8l/100km)
For shorter distance, for consumption matter it is better to brake also with the engine - but driver needs to be sensitive, otherwise the DMF flywheel may be stressed and this is very expensive part, this is why I do not recommend to brake too much with the engine.
For average driver - brake with the engine only when going downhill.