I've been trying to discuss this with someone from the LightSteamer technical department but it seems the technical support e-mail links directly to the sales team.
Currently there are 4 DotNet clients for LightStreamer.
None of these are compatible with Xamarin out of the box. Unfortunately because I don't have access to the source code I can't adapt any of them and recompile them as a PCL.
If someone from LightStreamer could port one of these to .NET version 4.5 in a PCL compatible format that would be ideal. I'm not sure if I have the technical expertise to implement my own generic HTTP solution.
I can confirm that at the moment the Lightstreamer .NET Client libraries are four, each specific for target platform:
However, it is expected in a short time a PCL version of Lightstreamer .NET Client library, with the intention to replace all the old ones.
Furthermore, it is also planned, though later in time, a UWP (Universal Windows Platform) library based on JavaScript.
I can also confirm that the Lightstreamer support team will contact you asap to let you know the ETA for the PCL lib.