What tends to happen is that the lanterns only move relatively slowly with respect to each other once they are high enough; they will only 'cross at different altitudes and occlude themselves' where the air is turbulent, which usually happens near the ground, soon after launch.
Once they are at height they are effectively fixed with respect to one another, and three lanterns will always form a triangle; no matter how scalene the triangle actually is, there will be a tendency for the observer to assume it is an equilateral or isosceles triangle seen from an odd angle. Even three lanterns in a straight line can be seen as an eqilateral triangle seen edge-on.
Our minds tend to look for regularity where none exists.