Anxiety can persist in lucid dreams depending on how conscious you are in them; if you're close to waking-life awareness you might feel some; if you're less aware you'll probably feel less. This anxiety may be amplified slightly because dreams tend to magnify our emotions and place them right in front of us. However, it may also be negated by the fact that you're dreaming. You have endless opportunities to do things like flying, and this might make you totally forget about your anxieties. Who knows!