You have made a lot of progress with the older girl, and you have been trying for two years with the ten-year-old. It's time to get some additional help with these issues with some family counseling. As you say, you don't want your stepdaughter to feel afraid of you, and a counselor can help all four of you work out what is going on in your family. The school counselor or your pediatrician can refer you to a therapist in your community.
In the meantime, try focusing on the positive with your stepdaughter. You've seen that punishing her does not work. Spanking her will absolutely not help and will only make her angry and resentful. Spanking is never useful, even with younger children, and it only teaches them to solve their problems by hitting.
Look in your public library or a bookstore for a book on positive discipline, and set up a system by which your ten-year-old can earn a check mark on a chart or calendar every time she follows a rule or does what you ask. With her input, determine what rewards she can earn. Five checks could earn extra computer time, and ten checks in one week could earn having a friend over to play. As her behavior improves you can increase the number of checks required to earn a reward. The key to any system like this is to use it consistently over a long period of time.
Lying is one of the most difficult issues for parents. It will be important to find out why your stepdaughter is lying, and the therapist you see can help you on that.