Carbohydrates are more easily metabolized than lipids. however, on a gram-for-gram basis lipids provide cells with more?

On a gram for gram basis lipids have the highest energy yield of all the food sources. 

Explanation; 
A gram of fat or lipids contains more than double the amount of energy present in a gram of carbohydrate. They yield 9 kcal of energy per gram while carbohydrates and proteins yield only 4 kcal of energy per gram. Most of the energy needed by the body is provided by the oxidation of carbohydrates and lipids.  Despite, lipids having more energy per gram than carbohydrates, carbohydrates are readily available. Additionally the conversion process is much less efficient because oxygen is required to burn fat.