I need to know about the factors affecting the biodiversity of the lionfish. These could include: niche diversity, area, climate, keystone...

The habitat of the lionfish includes warm, tropical marine environments especially in the South Pacific and Indian Oceans. However, they are also found in non-native habitats including the Southeastern U.S. waters and are invasive species in these locations.

The niche of the lionfish is that of a predator. Their adaptations include their pattern of coloration as well as their spiny fins. The pectoral fins can be used to corral their prey so they can consume them, although they move in a slow manner. They consume many different types of coral reef crustaceans and fish. 

Since they are adapted to warm tropical seas, if the climate should change and these areas become even warmer, this may adversely affect lionfish due to a possible decrease in their food supply. On the other hand, areas that were at one time cooler, may increase in temperature allowing lionfish to expand their territory. Pollution can adversely affect their habitat and food supply as well.

They have an interesting adaptation: venomous stinging spines which can cause great discomfort. Their spines and vivid coloration is a warning signal to other predators to keep lionfish safe from being consumed. They also grow to a large size rapidly to help them escape predation by larger fish.

In terms of being a keystone species, in their native habitat which is the coral reefs of the South Pacific and Indian Oceans, if they were to die off, the 50 or more species of smaller fish and crustaceans they consume would have one less predator to keep their numbers in check. Excessive numbers of the prey organisms would lead to increased competition for food and space and this could cause extensive harm to the ecosystem. Therefore, in their native environment, they are a keystone species.

However, in non-native habitats, like the Atlantic Ocean of the southeastern United States, these invasive fish can hurt grouper fish and other warm water predatory fish by competing with them for food or even feeding upon them. In this case, they become an invasive species whose effects are not fully known at this time.

I have included a link with excellent pictures of lionfish.