A lot of different factors influence dream clarity and lucidity.
Relaxing before going to sleep and/or going to sleep without being exhausted makes a difference.
How much you eat before going to sleep and how much time before makes a difference.
When you go sleep somewhere new or travel or did or saw something that made you automatically more attentive and aware, makes a difference.
Joshua Sw.:
I had some blurry regular dream where I was in a classical-inspired acropolis type area. I then had a profoundly clear dream.
Did you wake up between these dreams?
It is well-known in the lucid dreaming community that waking up after about 4-6 hours of sleep and going back to sleep considerably increase odds of lucidity, they even gave it a name,
WBTB(Wake Back To Bed).
Joshua Sw.:
My former teacher came to me, in the setting where I usually saw him in the past, and started asking me very awkward questions. About my career prospects and the like. He then sat down (like a scene change) and morphed into a messed up looking old man with no lips, just edges. His eyes were moving around like a snail's. I tried to leave, walking painfully slow past him, but infinitely slower and slower. I saw what seemed to be an angel of death in the corner of my eye. Everytime my focus turned away, I could see it's black feathery wings flap in tremendous clarity, and as soon as I looked directly near it, they disappeared. It felt exactly like the third jhana experienced earlier.
I never got too much into Dream Interpretation, it's a tricky business, it's too easy to fool yourself.
But be aware most of dream stuff is karmic, for example, you said your former teacher asked questions you deemed awkward and then changed form into something terrifying. A tentative interpretation(don't trust me) is that you are having problems yourself with these questions in your life, you find it awkward to deal with them, it was asked by someone you respected and/or find related to these questions(someone you think doesn't have these problems), but you didn't want to talk about it much and the figure and scenario became the image you have of these questions, your repulse of them.
Like I said, don't trust me on this, I just said whatever, only you can know for sure what the symbols mean and all.
While I certainly don't recommend as a primary practice, if you are interested in using your dreams to deal with karmic stuff, a book you could read is
The Tibetan Yogas Of Dream And Sleep