The idea behind a weightlifting routine when dieting is so that you can monitor your own strength levels while losing weight.
What I mean by that is, you want to be aware of what you're able to lift in your main exercises, and make sure your strength levels in those stay the same. If your strength begins to go down, it means you may be losing too much muscle during this diet and need to pay close attention to your diet.
A plan very high in protein will help to achieve this, while carbohydrates would be low or cycled, and fat would be in moderate amounts.
Also... cardio is pretty useful for losing weight. I would recommend doing 30 minutes after each workout, personally.
But these are just what I consider to be the basics as far as "cutting" goes.