Thunderbird/Lightning has been working with Google Calendar for a while now [cf. link]. however, Tasks are not supported as can be seen in this thread and also here.
now, is there another service for Tasks available?
for some time i have been using Chandler but with recent developments TB/Lightning+Chandler stopped working (and they haven’t quite figured out who’s to blame…).
ironically, Yahoo comes to the rescue: following this post and going further here Tasks with Yahoo actually work.