Thoughts in dreams

How do you experience thoughts in a lucid dream? Do they come naturally, kind of out of nowhere, but influenced by events/memory/senses? I've never had a lucid dream for more than maybe 10 seconds, so I'm curious. If I were to enter a lucid dream right now, that lasted for an extended period of time, would I be able to recall something that I could easily remember in waking life? Am I in control of my thoughts, or are they less influenced by me and more by my surroundings/subconscious desires? Could I "daydream" within a dream, where I visualize something in my head, and can picture it clearly? Does any form of concrete logic or "law" exist in lucid dreams?

Thanks in advance!
-Brees

To me the first thought that pops into my head is what I am usually thinking of the most when falling asleep. Recently that's been the task of the year, so the first thing that pops into my mind when I have a lucid dream. Thoughts or ideas normally just appear out of no where and I have to take a second each time I get lucid to really think about what I want to do. It seems that my inhibitions are lowered a great deal in lucid dreams so my brain sometimes thinks of things that have nothing to do with the situation.

As for remembering something, it's usually a little bit more difficult than when you are awake, but that's because not 100% of the brain is awake. It's not hard though to remember a specific thought, especially if you've been incubating it (thinking about it a lot during the day especially when you're falling asleep). The main problem I have is resisting sexual dreams. Many teenagers (such as myelf) have this issue due to going through/just finishing puberty, but if you train yourself a bit it's not that hard to resist these temptations.

Visualizing something in a dream is something that comes with practice. This is especially true when summoning an object since you have to picture it in your mind, how it feels, how much it weighs, how it looks, etc. Personally, after about my 10th LD I had no trouble with summoning things and I could do it fairly well by my 5th or so lucid.

Many things just take practice in regards to lucid dreaming. Just be persistant and don't give up and you can accomplish anything.