No, using invisible status doesn't make you a liar. Skype users know that invisible and offline status look exactly the same, so it's not even deceiving imo. Occasionally one of my language partners will complain about this, which is annoying. I don't complain about it, I just tell them the truth - "I always ask people with online status to talk first, so if you're invisible, I probably won't message you". I let them decide what they want to do, and it doesn't bother me if they want to stay invisible.
Another thing that doesn't make you a liar - using an avatar of someone or something other than yourself.
Naughty, naughty, naughty. Liar you are not, but hiding from someone you are.
I don't think you're a liar either. I leave my skype status as invisible when I don't want to be contacted directly but I do want to receive a notification if any of my contacts send me a message. I could put it as 'busy' or 'away' but I don't want them to think I'm ignoring them if they send me a message and I can't respond for a while.