After TB crashes, I put back lightning with the latest version 0.5 and so from the BirdieSync forum, I upgraded BirdieSync to 1.5.6.0.
Since, Cards and Files are well synchronised but not the Events and Tasks.
For the Calandar profile, I have no choice and so an empty profile for the calandar.
Please see logs files and screenshot sent by e-mail.
Anthony Grellier
Sync problem with no calendar profile
Sync problem with no calendar profile SOLVED
From Birdy advise, I had a look on the Error Console of Thunderbird, it appears that I had no name on the agenda folder. After naming the agenda, the problem disappeared.