When you have a calorie deficit, and you lift weights its mainly burning calories and aiding in burning fat, correct? You are not really gaining any mass unless you eat an excess in calories, right?

If anyone could correct me or provide any extra supporting details (while I read up on it myself) that would be awesome.

(family argument )

The only way you "may" gain lean tissue is if you are VERY new to working out however it's not likely simply because the material for growth is not present. Even when the material is present, it is a very slow process to pack on lean mass.

it happens that when u start to work out, u maybe get few kilos, even on diet. simply because muscles are heavier then fat. for example, i am dieting and working out (cardio 1 hour + weight lifting 1 hour x 4 times a week), and i lost only 2 kilos last month and i droped one size-----

If the body has what it needs, it will build muscle, but unless you are a body builder or already very fit, I do not see why you could not burn fat and build muscle at the same time. Personal opinion.

Well it's hard for your body to put on muscle, when it's getting a deficit of calories. At the same time, it's hard for your body to shed fat when you are getting a surplus of calories...really pretty simple.

Lifting is crucial while cutting though, simply to maintain the muscle you have. It's easy to monitor as well, your lifts should stay the same the whole time you are losing fat, that way you know it's effective and you are not losing muscle.

I put on muscle last spring while losing 30 lbs in 3 months between running every other day(multimile5-10 range) and doing resistance workouts on my totalgym, not a lot be it, but toned up and added a bit to me.