The above comment is mostly right, but you also need to enable MCU in Reaper's settings to achieve full functionality. The complete list of things you need to do are as follows.
Step 0: Click the DAW button, then click it again and hold. Where it says "Daw Mapping", scroll until you see Reaper. Click the Scroll Wheel to select it.
Step 1: Use CTRL + P to open up the preferences menu. (Options>Preferences)
Step 2: Under Audio, click MIDI Devices, and double click "KeyLab mkII 88". Make sure both squares are checked. Hit Apply to enable.
Step 3: Scroll all the way down the side bar. Click the category, "Control/OSC/web".
Step 4: Hit "Add", and under the Control Surface Mode dropdown, click "Mackie Control Universal".
Step 5: For MIDI Input, choose "MIDIIN2 (KeyLab mkII 88)". For MIDI Output, click "MIDIOUT2 (KeyLab mkII 88)".
Step 6: Hit OK to exit the preferences menu.
Now your transport and faders should all work, and everything should be mapped correctly for as long as you are in Reaper mode under the Daw button.