Since the lion fish became the apex predator in the controlled environment, I will balance the cycle by adding a (1) new predator which typically feeds on a lion fish and (2) another predatoir which preys on the predator which eats lion fish and preys on lionfish (which unquestionably preys on the lionfishes' prey too).
This method is effective because in every experiment, there is always a control. The control speciment will be the predator which preys on the lionfish.
Development can be noted if and only if the populatyion of the lionfish is decreased. If it happened and it will happen, the population of the two predators I added will be decreased proportional to the number of the lionfishes around.
Using integral calculus: Exponential Growth and Decay, we will be able to track down clearly the population of each species in the controlled environment.