I want to use my Facebook/Youtube live streams in my channel.
I want a live stream in my channel using my live stream from Facebook/Youtube.
I want my Live stream content to always be live.
Roku supports HLS and DASH formatted live streams.
Most likely you will need to use a streaming service such as ScaleEngine, Akamai, BitGravity or Amazon - there are many others and most that would be usable with a Roku are not free. Youtube and Facebook usually don't allow you direct access to the stream URL, but instead use their own player to play content.