We advise not lo attach Chinese flying paper lanterns to a rope, it can cause dangerous situations, after all a sky lantern is designed to fly free!
We from time to time use this technique in order to make pictures of the lantern while it floats in the air. But then again, we work with lanterns for about 10 years now which makes us experts, we know how to handle them.
In the absence of wind the risk is small, the lantern will rise and stay more or less above your head.
If there is a gush of wind it is a different story, the wind will try to make the lantern move sideways, the wire will block this movement and make it tilt. The flame will remain vertical, the lantern will be tilted, the flame will touch the paper. Our lanterns will not catch fire since we use fire retardant paper, but being very thin paper the flame will burn a hole in this chines paper lantern making the hot air escape and the structure fall down with the fuel cell still burning.
Don't try this at home!