This has been fixed yesterday, please try the nightly builds of Lightning.

My TB 3.1 with stable addon and sogo 1.3.1, no button.

My users don't discriminate between invitations comming from SOGo and other systems. Users don't
understand why they can accept some invitations and cannot accept some others. They don't understand
why it works in SOGo WebGUI mail module and doesn't work in TH mail.
They consider it for an instability or for a bug.

To accept/decline invitation directly from TH mail is ergonomic for them. Switching to calendar
view, finding event and then accepting it there is not comfortable for them.
I agree with their view on this point ;-)

It's an open bug i think.

The problem was fixed for me with the nightly build on 10/13/2010:

lightning-1.0b2.102i_linux-x86_64.xpi

Lightning 1.0b2.103i (released with 1.3.3) isn't fixed
I don't understand.

I would also like the Buttons to be visible in the Mail.

I tested with SOGo 1.3.3 and Thunderbird 3.1.4 (and 3.1.5) und Plugins *.103.

Invitation from other SOGo Users are shown directly in the Calender (dotted Line arround the Event) and the Buttons are missing in the Mail (in TB).
In SOGo's Webinterface the button in the Mail are visible.

Invitation from external Users shown ok. The Buttons in the mail are visible in TB and the Webinterface. The Event is not shown in the Calender.

As Allesio wrote above, Users don't understand, why the Invitations are handled differently.

Fixed with http://mtn.inverse.ca/revision/diff/62428aecc62d07f592f24bea5c7c95be9ebbd33e/with/0783a20aa83c4249f0483151882ca4d7ff6cf4e7

Try out the 1.0b2+105pre1 version from http://inverse.ca/downloads/extensions/nightly/

The patch was reverted a few weeks ago.

Apparently, the patch was reverted as it affected how other providers calendars, ie Google calendar worked with Sogo.

This problem is quite a major issue for us and we badly need it resolving.

Although its a faff, its it straightforward to take the patch mentioned above and apply to your lightning builds. The patch fixed our problem with email invitations nicely. We are not concerned with how external users interact with our sogo system, so if the patch creates issues with them, it doesn't bother us.

Fixed in revision 634f256972e1b5df91beb63a9c6df13a66e9d472.