When should the battery in my 2008 Lexus RX400h cut in?

There’s no simple answer to this. The computer program that controls when the hybrid system chimes in to help with the petrol engine is a very complex one and depends on a lot of inputs. For instance, the driving mode you’re using will vary this, so will the amount of charge in the battery at the time and even how aggressively you’re driving.

As time and kilometres go by, the condition of the battery would also probably make a difference, as can what accessories (air conditioning, for instance) you’re running at that moment in time.