No it doesn't work that way. It's not the fat you need for weight lifting it is the muscle glycogen. That is why you do the weights first. Women might burn fat slightly more slowly then men because of lower testosterone levels, but they don't have to do anything different.
I have trained females before. They respond to the same thing as males. Low carbs, lots of protein, lifting heavy, and adding intense cardio and or anaerobic intervals just a little at a time causes steady weight loss at a decent pace. Muscle is spared for the most part. Or in the case of beginners they put on quite a bit of muscle at the same time.
To bulk, same thing, but do virtually no cardio and kick the carb intake up.
Think of your energy as a barrel of wine. You drink most of it and then dump out the dregs. You don't want to dump out most of it and drink the dregs. So you use the energy and then waste the excess, don't start by wasting and then try to use the end of it. Like I was saying do warm up sets. Don't lift cold.
If you can do cardio as good after weights as you can fresh, you didn't do what you needed to do with the weights. If your trying to lose weight. When you are on a cutting type diet, by the end of your workout you should be pretty shakey, because you've used up your glycogen. Then you go a little further by pushing yourself through some intervals.
Weights are exponentially superior for losing weight. Cardio isn't even icing on the cake. It's like that little frosting dot over the i on a happy birthday cake.
Here is a very good explanation by Alwyn Cosgrove.