This might be a wrong take on LOP, but the thing is that LOP has not
stabilized enough yet so that people have a common language  about it.
I personally tend to agree to JetBrains' view on LOP, and their MPS
system in which LOP comes as a language design tool as compared to a
language mixing tool. That is, it gives an environment in which one
can define a DSL for each problem domain  in question. In any events,
thanks for bringing this up and I appreciate if you fill me in with
similar stuffs. My nerdy side is kicking in....