I am working on a similar project.
It seems to works well with loopMIDI and LoopBe from directly in Reaper, but you need to be specific about the channel mapping and go slowly to make sure that you can make it happen.
I recommend LoopMIDI because it is freeware, so install that first.
Set up the source and get it working well with your lights in LightJams - first with direct mouse control or wave control (using a wave pattern or the little hand). I have found that it is easiest to work with a simple light at first.
Make sure you can trigger the power and get the light effect that you want in LightJams directly, and then with a local MIDI controller (View -> configuration -> MIDI tab). I am using an APC 25 or an APC MIDIMIX, for example, so I make the effect happen with the buttons and sliders directly in LightJams first, before proceeding to Reaper.
Next is the Reaper part.
Start with a simple project! One MIDI channel to start with to make sure you know what the heck you are doing. Paint some MIDI notes, or even better, use the same controller and notes that you used directly in LightJams.
Set up the MIDI send to use the same channel you used in LightJams in channel properties.
Make sure you are sending the MIDI and CC messages out of Reaper to the LoopMIDI software from Reaper, and then set LoopMIDI as your input in LightJams.
You won't be able to have your device working simultaneously in both programs, but you can pass all of the events and controller data through with LoopMIDI.
I'm really grateful to Mathieu for the the OSC VST plugin, but it seems to be overkill for what most users are up to. Maybe I will need that for a future project!