LPC826 - Case Pisitive or Negative?

My guess is some sort of feedback component in the laser diode. We don't need it to function so we mark it as "not used".

Some diodes have a builtin photodiode which uses the third pin. Some are dual red/IR with the positive
for the IR usually on the third pin. Some diodes even have four pins. IIRC, there is even a tricolor diode
floating around out there that has 405, 660, and 780nm in the same package. The ones with the
photodiode are usually low power. They were used in CD players to stabilize the output. "Feedback"
as you say

Leaving pins physically present when unused is standard practice in the semiconductor industry. The
5.6mm package is an old standard and even predates diode LASERs. To just leave it out could
possibly require special tooling and complicate the design process, so it is just left in. Some of the
new Nichia diodes have unusual pin locations, so it does happen, but if a designer sees two parts which
are identical in every way, except one of them has a non-standard footprint, you can guess which one is
going into the final design.