Grease two 20 cm (8-Inch) nonstick springform cake tines and preheat the oven to 180 Celsius (350 Fahrenheit).
Grate the carrots using a food processor and remove the grated carrots from the bowl and set aside. Remove the grater attachment from the food processor and switch to the chopping attachment and add the pecans and pulse until roughly chopped. Set aside with the carrots.
Add the remaining cake ingredients (except the carrots and pecans) and process to combine. Finally, add the carrot and pecans and pulse to combine with the cake batter.
Divide the batter between the prepared springform pans and bake for 15 to 25 minutes. Remove from the oven and let the cake cool completely in the tin before removing.
To make the frosting combine the butter and cream cheese in the bowl of an electric mixer fitted with a paddle attachment and beat until smooth and creamy. Add the icing sugar and lemon juice and zest and beat for another 5 minutes, or until pale and fluffy.
Spread the frosting between the cake layers and over the top of the cooled cake.