Please note that the current bluz firmware is based on 0.5.X of the Particle branch. This means that if you are compiling something on the Photon with 0.6.X that there may be features that aren't yet in the bluz firmware. Specifically in this case, there is this: https://github.com/spark/firmware/issues/1278 which adds Arduino.h compatibility. Before the upgrade to 0.6.0, everyone in the Photon world had to remove Arduino.h and Wire.h library references, just as you do now.
We plan to upgrade our firmware to 0.6.0 in the near future, but it is not a small effort. Things change pretty rapidly and we are trying to address our own BLE based features and stay on top of Particle releases, it is quite a lot to balance.
To get your specific library working, you can do the following. Remove all references to Arduino.h and Wire.h, and in LIDARLite.h, replace them with:
#define bitRead(value, bit) (((value) >> (bit)) & 0x01)
#define ARDUINO 158
Then, in LIDARLite.cpp, you need to fix one line as the Particle 0.5.0 firmware wasn't compatible with Arduino, so change this line:
Wire.setClock(400000UL); // Set I2C frequency to 400kHz, for Arduino Due
Wire.setSpeed(400000UL); // Set I2C frequency to 400kHz, for Arduino Due
With those changes, I can compile this library (though I can't test it since I don't have this device).