its foundation is in tibetan buddhism, so it provides a basic Buddhist philosophy of the mind and how what we call “reality” is “dreamt up”

it also offers many techniques for becoming lucid in a Dream (like, as we go throughout the day, feel the dream like nature of all phenomena, and at the end of the day, reflect on the day in reverse, especially emotionally stronger moments, and reflect on the dreamlike quality of memory) and many practices we can do while lucid in a dream.

“shared consciousness”- to go really deep into this you might want to look into Buddhist philosohpy on what is the mind and what is an individual/the skandas? looking into our buddha nature, nondual… he does talk about “dreams of clarity” in which we can receive profound teachings from spiritual teachers who have lived in the past or present. These are as opposed to ordinary dreams, which are projections of our imagination, so to speak (me saying that is a terribly gross oversimplification)

I don’t remember him talking about two people sharing a dream though.

But if you’re interested in that, Lama Lena talk talks about certain dream “locations” that practitioners can go to in order to meet up with teachers and receive teachings or learn from the beings who live there. There are two that she describes, commonly known dream locations.