Something has changed in the way that LG handles logins. TheShark can't connect to check for invites, either. I hope to look into this further in the near future. I'll keep you guys posted if I figure anything out...
There was no change in the api, but only a small change on the page. The little red icon next to the number of pending games is now refreshed regularly, so when your opponent pulls it will be reflected on the icon and no refresh of the page is needed.
The list of games can be retrieved through the api interface. There is no need to parse the page. The api is not public but you can contact me and I will provide it.
The same thing happened to my Amazons bots. My scripts load the index page and then get the game IDs from that page. Now, though, the game IDs appear to be loaded with AJAX, so my bot doesn't see the game IDs anymore.