The page Prophecies of the Shadow describes a theory about Lan being the Broken Champion.
Argument against that:
The Lord of the Evening and the Lord of the Morning (Ishamael and the Dragon ) are both bound to the Wheel. They are continuously woven back to the Pattern Age after Age with their remembering soul. Ishamael always remembers to everything what was and what comes, while the Dragon is doomed to a slow process of gaining back his memories and more times he fails then succeeds. (ref. B2.ch37)
"We are tied together as surely as two sides of the same coin."
Demandred might be also bound to the Wheel, Forsakens' knowledge and life circulation is unclear to me. But Lan definitely isn't so he cannot be the Broken Champion. Most likely the Broken Champion refers to the Dragon in the interpretation of Shadow – of course – they expect him to be broken by that time.
Both Prophecies cannot be fulfilled at the same time. Actually, only the Prophecies of the Light can be fulfilled at all – and must be fulfilled to reach the end of a certain Age. When the Prophecies of the Light are not fulfilled, the Champion of the Light simply fails and the Pattern starts to weave another thread for him. (Supporting evidence in B2, Ch37 - Rand lives as many lives, he always feels his fate, he never falls for the Shadow, only dies without reaching his purpose. No matter he hears Ba'alzamon's voice: "I have won again, Lews Therin." , actually the Shadow never wins in this way. It is just a temporary, small victory, and from the Light's perspective, only part of the way to get to the Light's Victory. )
Since the fulfillment of the Prophecies of the Shadow would certainly mean the victory of the Shadow and the Breaking of the Wheel, the Breaking of the Time, logically it means that they were never fulfilled before and by the nature of the continuous balance of Light and Shadow, most probably it could never happen. The Light always wins at the end. When it fails, that is just part of the way to its victory.
Neither there is a final victory for the Light. The Balance requires the Light and the Shadow and the possibility of choice to humanity.
Brandon Sanderson revealed that "Everything in the Shadow Prophecy did indeed happen.", so I will revise this post soon. :)