The adiabatic flame temperature is the temperature that a gas will reach when combustion occurs in an insulated system with no heat loss. The adiabatic flame temperature is highest when the combustion is complete and occurs adiabatically (without heat loss or gain). This ensures that all the energy released by the fuel is converted into thermal energy of the combustion products.
In the case of incomplete combustion, energy is wasted as unburnt fuel, and heat loss can occur in real-world systems, reducing the maximum possible flame temperature.
The lean air-fuel ratio refers to having excess air in the mixture, which reduces the amount of fuel available for combustion and thus lowers the flame temperature.
Thus, the correct condition for the highest adiabatic flame temperature is when combustion is complete and adiabatic.