I hope everyone realises Skype was a POS long before Microsoft bought the company.
On performance; If you're running a bomb PC then it is basic common sense that newer version probably won't work well with your PC.
On Skype lag; Do as Zelot says. I bet 99% of your logs are useless trash that is no good to anyone, so save what you might need in the future and bin the rest.
on the Skype menus at the top left, click on Tools and select Options. In the box that comes up click on Privacy and look in the Privacy Settings menu. Third block down, on the right, is a "Clear History" button. Press and your history will be cleared. In that drop down next to it you can select how long to keep history for too. I use the "2 weeks" option.
At any rate, I have noticed lag caused by Skype too and have made it a habit of turning off most other programs while I'm in game. Seems to help quite a bit and I don't get tempted to alt-tab out to find out what all the beeping is about.