For lasers used for free space / mirror steered / diffuse beam communications or LIDAR scanning, would there be some way for a single laser to be able to selectively transmit across a range of colors, to a receiver that can similarly distinguish between colors?
This would be similar in operating principle to a radio transmitter that can adjust its transmitting frequency up or down across the radio spectrum, to a radio receiver that can distinguish what frequency it is receiving.
There's very different kinds of lasers, and while there's tunable lasers, these really don't belong in the category of things you mount on a LIDAR scanner, at all.
So, no, no adjustable lasers themselves.
You can, however, frequencymix lasers with laser, and lasers with RF signals, and do all kinds of crazy photonic things. But: either that will be very discrete (mixing laser with laser: you can only get discrete lasers) or far below what you'd call "a range of colors": If you use a really high-frequency (e.g. 60 GHz) RF signal to modulate a red laser (say at 400.000 THz), then the resulting color will still be exactly as you can optically determine without mixing coherently with the original laser: red, the exact same red as before (now at 400.060 THz, congrats).
Through the magic of nonlinear optics you can buy a super supercontinuum laser which outputs light in a very broad spectrum, typically 400 nm to 1,700 nm.