According to Meera, the Knight of the Laughing Tree was, "short of stature, and clad in ill-fitting armor made up of bits and pieces" (III: 283). This limits the possibilities some what, as any one of average or greater height can be immediately ruled out. The mish-mash nature of the armor is not necessarily a clue; it might well indicate that the Knight was someone who had not expected to enter the tournament and thus had to scrounge armor, but it could be someone who purposefully scrounged armor to hide his identity.
Of the candidates, almost all of them are either known to be small or to be quite young. Eddard Stark has been considered, but he was 18 at Harrenhal and seems to have been of average height, which rules him out. The laughing weirwood on the Knight’s shield also seems unlike Ned, though it may be an attempt to throw off suspicion. Howland Reed has strong proponents, despite the clear references to the fact that he knew little of jousting, much less of riding horses. Those who support him as the Knight suggest that the green men of the Isle of Faces may have assisted him magically. In a similar vein, it’s been suggested that the Knight was in fact a green man, which cannot be refuted for lack of evidence.
Another candidate who has been put forward is Benjen Stark. We know he was present and that he was certainly young enough to be the right size. He also would have had training from an early age in horsemanship and jousting. The mish-mash armor would fit him as well, as he scrounged for pieces of equipment which was likely all too large for him. However, given Benjen’s storyline in the series and the way Jojen emphasized how it was strange that Eddard Stark never told this tale to his children (III: 279. 284), it seems difficult to imagine that this fits. In a similar vein, a young Sandor Clegane has been mentioned. Besides the same objection as with Benjen, it’s unclear that a young Sandor would have been small enough to be "short of stature". It would also be unlikely for him to settle on an image of a weirwood.
The final, and most popular, possibility is Lyanna Stark herself. She had already acted to defend Howland Reed (III: 281) with a notable fierceness. It’s been noted that she was a very skilled horsewoman (III: 193, V: 547), and previously Ned noted that she might have carried a sword if Lord Rickard had allowed it (I: 186). ASoS is also the novel where riding at rings—which was certainly done in preparation for learning how to joust—is a common pastime for young squires (III: 493). Put together, it has been suggested that Lyanna Stark was allowed to sharpen her horsemanship abilities by riding at rings, giving her at least preliminary training for jousting, which is more than Howland Reed ever had. The scrounged armor needs no explanation, though here some suggest that she had her brother Benjen assist her—primarily due to the notion that Benjen may have joined the Watch in part to escape his feelings of guilt over what transpired afterwards. While Lyanna-as-the-KoLT would require a great deal of luck to defeat three knights (even though their level of skill is unknown), it’s not entirely out of the realm of possibility.
The main reason this theory is popular is that it would help to explain what is believed to have happened with Rhaegar. It’s explicitly stated that he was ordered by the king to find the Knight. Rhaegar may have done so, but admiring her courage and honor he kept her secret. This would also be an exceptionally good reason for why he crowned her the Queen of Love and Beauty as he did.