What was the purpose of the lightning tree?

This is explained a little more in the Novel, and is easier to understand with the hindsight of knowing Plutarch Heavensbee was subversively finding ways to assist the tributes who were complicit in the revolution...

It doesn't explicitly state 'Plutarch did this because of this and this...' because that would be terrible clunky writing, and Collins is a much better writer than most people will give her credit for... it just takes a little logic and deduction.

The 'Lightning Tree' is in the section of the Arena which endures a lightning storm within its hour. The lightning tree introduces (naturally, without raising the suspicions of anyone else) the element of controlled, predictable burst of electricity in a pre-designated location, which obviously is of benefit to Beetee.

Furthermore, it is a clear and concise way for the tributes to keep track of what time it is, even if they aren't anywhere near the section that is enduring it's 'hour'. It's the equivalent of Big Ben striking 12.

It's never pro-filmically shown that Beetee had discussed a plan with Heavensbee beforehand, but it's interesting that Beetee is insistent on carrying around that spool of electrical wire throughout most of the film. It's quite an encumbrance to keep hold of, 'just in-case', so it could be inferred that Beetee had the plan all along.

Note that Heavensbee, the current gamemaker, is in fact working for the insurgents. He would have absolute power to decide to create something like a lightning tree, for Beetee to use. And since its hazardous nonetheless, it doesn't raise any other official's eyebrows.