Basically the engine will not be running efficiently, making less power at any given rpm. Lean mixtures tend to want to "explode" more easily, but in an uncontrolled manner (pre-ignition etc), hence the reference to engine damage.

If the air fuel mixture is too lean, it won't ignite properly and you will have wasted that particular charge of air/fuel. To compensate, wider throttle openings need to be used to maintain an equivalent road speed to that on a correctly fuelled engine.

Essentially the motor will be running way outside its zone of efficiency, which equals poor economy.

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