Can LD help you overcome fears/phobias?
It sure can 
. When you become lucid (and you feel you’re ready for it), ask to confront your fear. When it shows up, demand to know why it is trying to ruin your life. If needed, beat the living daylights out of it. It’s the same basic technique you would use if you became lucid in a nightmare.
Definitely possible. I used LD’s to get over my fear of daddy-long-leg spiders. It was a terrifying experience, but it was well worth it.
Are you kidding? Lucid dreams are one of the best means there is to win your fears! 
You just have to ask the dream to face one, then proceed like it was a nightmare, which means you can read LDphone’s guide or the appropriate part in my own guide to know the details.
With my best wishes for your personal growth. 
Man, spiders takes guts! 
One day I’ll give it a try too… sigh one day.