I have not heard anything about how it integrates with Skype but I haven’t been using Skype for a while.
I use Lync and like most Microsoft products it’s generally terrible. It’s designed to be usable through a web client, but in my experience it still has lots of bugs, stability issues, and cross platform issues especially with Macs (regardless of if using the native or web client).
If you are just joining the meeting you should get sent a link to join - you should be able to click it before the meeting begins to load the web client into your browser. You should be able to give it a shot before the meeting starts.