It will not run the LOR software since I believe that is windows based.
The Model 2 might. I haven't tried it, but the Raspberry Pi 2 runs Windows 10. (I don't particularly recommend it, but someone here might give it a try.)
The application that most (probably ALL) people run is the Falcon Pi Player (FPP) (You are not allowed to view links.
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No, definitely not all. My outdoor Christmas show runs on FPP, but my Halloween show runs on QLC+, and my indoor Christmas show runs on Open Lighting Architecture.
So in general, you can continue to sequence in LOR's app, use xLights to convert to FPP format (I think they are .fseq files), upload to the PI, setup your hardware configuration in FPP (tell FPP what protocol, channels, etc), schedule and run.
Absolutely. Vixen has a built-in FPP export utility, as well, and it's what I use for the outdoor Christmas show. 'Lots of options from which to choose.
The setup of FPP is extremely simple. Takes about 3 hours to download, install and configure.
Rather less on a Pi 2. It has a lot more horsepower than the Model B.