Using vegetable oil instead of lard is a supremely bad idea. Vegetable oils contain polyunsaturated fats that become oxidized in your body. In addition. vegetable oils, with the exception of olive require industrial processes to manufacture them.
The fatty acid profile in lard is very similar to olive oil. The fatty acid profile in vegetable oil, which is probably soybean oil, is primarily polyunsaturated fatty acids.
Eating fat when restricting carbohydrates is actually healthy. Also keep in mind that there are protein-deficiency and fat-deficiency diseases. There are no carbohydare-deficiency diseases.