I'm sorry that you are dealing with this. It's so hard.
my experience is that all of my kids lied at age 6, even the oldest who was 6 when my AH wasn't yet drinking. All of my kids were affected by living with an active alcoholic. They grew out of lying but they will never grow out of being children of an alcoholic. Therapy is an option. There are also many library books about family addiction that helped my kids to talk about what was going on and how they felt. If you go the therapy route, be sure and get someone skilled in dealing with alcoholism and not just trained to deal with children.