Lady Gaga might have a Skype account but she wouldn't make it public for everyone to know it. If she does have a Skype, she probably only gives it to a few people who she wants or needs to chat or video conference with.
Has Lady Gaga made her Skype details public?
She has never released a name or profile to the public for the video conferencing app, so she probably doesn't want her fans or everybody else to be able to contact her on there so easily.
Can you imagine if anyone could call Lady Gaga on Skype when they wanted to?
She would probably get calls and messages non-stop... not only from people who adore her, but probably also people who don't like her and have nothing else to do with their time than annoy her.
As with most mega-celebrities, the best ways to get to them nowadays is through their public social media accounts.
Here are some of hers:
Twitter - http://twitter.com/LadyGaga
Instagram - http://instagram.com/ladygaga
Facebook - https://www.facebook.com/ladygaga
