Lucid Dream Traveler

I do not think so because all the rules for physically entering a dream follow the physical world. And since the dream exists inside the head of the dreamer it would not be possible for them to physically enter their own head. And you would transport a sleeping person into a dream. They would till be asleep.

I do not think you can stick someone in imagination. I think the traveler must find the gate to that area.

Given your scenario you could have spiritual travelers do that but not physical travelers. And you would need a third person casting the spell for spirit travel in the dream since all your magic falls to imaginem. And while both travelers could be in each other's imagination, neither one could wake up without leaving.

I've always seen Glamour magic as like being a "real-world" version of what you can do in dreams (using Imaginem to simulate any form except Mentem) but with the weakness that it can be undone by some means - iron, religious symbols, some other common ward against fae. In dreams, every hermetic magus is like a Glamour mage, but with the limitation it only affects you in the way dreams do. So a Glamour mage would be able to do exactly like they do in the normal world, but still having their usual limitation, while a regular Imaginem specialist wouldn't have their magic undone just because someone knows the folk remedy against them. The main advantage a Glamour mage would have is that they would have formulaic Im spells already in place to mimic the effects they want.

Can a spirit traveler, going into their own imagination, lucid dream within that realm?

Yes. since all rules that apply to dreams also apply to imagination.