Why don't I have access to my Google Calendar tasks using either Lighting for Thunderbird or Evolution?
I can sync calendars without any problems, but I do not even have read access to tasks...
The reason is because Google has not created any functionality in their Google Calendar APIs for doing anything with tasks. Without an API for this, applications would have to screen-scrape, which is a pain and is inconvenient.
Many developers want such an API, so such functionality will probably be added soon.
Until then, there's not much you can do. Sorry!