can you have lift without thrust (to the outside atmosphere)?

Although there are many descriptions of how a wing works, there is one, and one only, condition.

The air after leaving the wing must have its direction of motion altered.

This is just one form of the principle of conservation of momentum.

Hence your analysis must simply look at whether at the rear of the box the air may leave it in a downwards direction.

If it can then the device can produce lift. If not, then it can't.

The details of the box or the airflow inside it are not relevant in this context.

In terms of efficiency though, the wing is trying to force the air downwards. But if there is a solid box below it then there is an upwards pressure from the wall of the box and the wing would be less efficient than if it was in free air. Even if it can produce SOME lift.

So to your question. Unless it moves the outside air it CANNOT produce lift.

Hence, no thrust, no lift.

It wouldn't work since as the jet is blowing the wing, the wing is also being weighed down by the rest of the box. Just like the attempt to create working cars by attaching magnets in front of them (attached to the car) that attract the car.

What you seemed to have described, although the design details need a little work, is a wind tunnel isn't it???

no