What is the reason for on and off lucid dreaming?

First of all, No! You are not in-love with this other person you are simply missing his energy. And the name is a kind of a constant reminder. The fact that you did go back in time before your cat died shows that something happened in the past that left its mark and you’re subconscious is trying to point this event out to you. This might be a day when something significant happened. This thing in your past might be reoccurring this will explain you trying to rescue your cat by taking her from the past and into your future or “future past” if you will. I don’t think your cat is a bad omen in this scenario after all you are trying to rescue her. Your pregnancy plays around with your emotions and will explain your vivid dreams. Your visions might be something else. It can be related to your physical state of not sleeping a lot and it might be random. I think you need to relax and meditation can help. The spirits I think is showing you that you are sensitive but I recommend you close this door for now. It can be good to talk to them and it can be bad to talk to them not all are peaceful. Write your dreams down, and make notes of the black and white dreams and the colourful dreams this might point to something we are missing. Good luck and be safe.