It doesn't increase the process -- but it does make it more likely that the existing processes will burn some fat.
But the point of lifting is usually to grow muscle. The effect of lifting will burn calories for MANY, MANY hours after the lifting. But in the short period immediately after lifting, the muscle will quickly take up protein and carbohydrate by way of recovery, which makes it an optimal time to feed the body, even if you're reducing the rest of the diet for fat loss.