I have heard a theory that lucid dreaming practice will make you more aware of yourself and your emotions, so that you could actually choose on a much greater level what mood you want to be in.
For example, if you feel mad about something or are bothered by something, you could much more easily control those emotions and avoid getting angry or frustrated.
Is this true?
I have never heard of this theory before but it does sound interesting. I don’t think lucid dreaming itself has had any effect on my ability to control waking life emotions. I bet there’s some way to use lucid dreaming to aid in emotional control though. I remember I used to have a lot of stress, anger, and other negative feelings built up inside of me in waking life. I think that because of this, I sort of developed a power in my dreams that I call “fury mode”. With this power, I release powerful emotional energy, which I use to fight monsters. When I wake up from dreams where I use fury mode I usually don’t feel angry anymore. It’s strange, but it seems act as a safe emotional outlet.
Well, your method certainly seems like a good way to control your real-life emotions. 
I believe the theory behind the statement in my original post was that lucid dreaming and awareness will make it easier for you to notice your own feelings, and be able to question them and control them much better.
Something like that.
I haven’t noticed a difference in my ability to control my emotions simply from my awareness. I just thought I would mention the fury thing since it was similar.
Personally I’ve found that lucid dreaming has given me the conviction that I can control my experience as it is all created by me, not just in dreams but in waking life as well. In this way I think it’s given me greater control over myself, so yeah, I think this theory is a good one 
Yeah I believe it should have an indirect effect on your ability to control your own feelings, since that is a form of awareness. 
Another thing I have noticed among lots of people is that they tend to startle and quickly observe people who suddenly appear close to them - could this have something to do with “day-walking” and a lack of a lucid mindset?
Because I know that ever since I started practising LL I have pretty much never been surprised when people appear, I have always heard their footsteps or expected them to be there or had their presence given away in some way since I always try to pay attention to my surroundings with all my senses.
Yes there are some Emotional Benefits of lucid dreaming. Dreams can carry over feelings into the waking world – just as a nightmare can induce stress into your daily life, an inspirational dream can keep you happy and motivated throughout the day. Many people use lucid dreaming techniques to give themselves that needed kick to jumpstart their day.