Regarding "raw data" and internal representation/algorithm used: see specifically patent application 20130182079 (above). The LMC hardware is just two cameras with a Cypress FX3 USB3 controller, read as a simple USB camera:
The Leap controller itself apparently generates pixel-by-pixel interleaves stereo images, all further processing is done on the host PC. The basic idea is to reconstruct edges from edge pairs in scanlines in stereoscopic images. This means that it is well suited to scan convex objects without self-occlusion, i.e. objects that can be represented as ellipses or circles arranged in a manner that avoids obstruction/occlusion. To reconstruct a hand, you have to identify fingers, and then attempt to fit a hand skeleton to the reconstructed fingers. While hands all have the same topology (barring missing or completely occluded fingers), adding tools will make the problem of matching much more challenging.
There are no depth maps, no point clouds etc. Here is an image that illustrates the "capture" that the Leap Motion (according to the patents) generates:
Any point cloud or mesh representation is in turn created from the skeletal match. Note that the per-slice reconstruction of ellipses does not lend itself to handling the palm.
For reportedly raw imagery see here
The video streams of the two cameras are pixel-wise interlaced:
The Leap is a straight-forward stereo camera. The Leap software attempts to reconstruct fingers from silhouette edges, and attempts to reconstruct hands from fingers and possibly palm edges. The raw data is pairs of images. To implement your own software stack to process the "raw" image data, you might want to start with something like
as the SDK offers no API to obtain just images, let alone contrast-enhanced/background-eliminated images. There is also no API to simply obtain per-slice edge and/or reconstructed ellipse information, which would be ideal to optimize for tool-only use cases.