Yes, the bracket will attach to the notebook tray.
There are a couple things to note: The bracket will apply extra weight to the arm and reduce its capacity. Also, the back of the laptop cannot overhang off the back of the tray because the release tab will protrude above the tray--this may move your laptop further down on the tray than otherwise would be the case. That matters only because it could end up applying more force on the arm's pivot and reduce capacity a bit further.
Long story short, if your laptop is not toward the upper end of the arm's weight capacity (in ordinary circumstances, the capacity of the LX Arm when holding a laptop is 12 lbs), you should have no problem. And yes, you will need two brackets.