I was wondering if this was possible:

Using a RotS Lamprey with a JJ infantry in it at cruising.
Give the Lamprey a move and shoot order.
As the the moving part, use half its speed points to deploy the infantry its carrying with it. Use the other half of the speed points to move and shoot a target.

Speed (at primary): 17
Weapons range: 0/8"

-Spend 12 speed points for a move and shoot order (down to 5 speed points)
-Spend half of remaining speed points to deploy infantry in transport (down to 3 speed points)
-Use remaining speed points to move 3" and shoot at a target

Is that legal, or is it too good to be true?

no, because you have to spen half(rounded up) of it's printed speed value, so it costs you 9 to unload. A vtol would have to have a move of at least 24 to be able to unload and shoot. (12 to unload, 12 to shoot)

Bahoom is correct.
The best you could do (and this goes for any transport) is push to fire and hope it salvages you.