Hey, Davood!
"I never tell lies to my parents" is correct. Because you are talking about telling lies, about the action, to lie. And you never do that.
About the other examples, "To read a story" indicate that you are talking about read one story. Whereas "To read stories" means you are talking about read different stories in different situations, for example:
Let me read a story for you.
or
I always read stories for my son.
I hope this helps!