Please discard this issue.
Today, it's working fine.
Probably it was a cache problem even though I'm quite sure I deleted it.

This is still an active issue. I tried upgrading directly from 2.05 to 2.65 Notifications table was not there. I am trying to create the table from my dev to push it along. I will see if it works. PS, I had no problme on dev

Here is what I did to get around it
The first notification was that the table notifications did not exist. Error indicated above.
We created the table from the table schema from our development upgrade.
The upgrade continued until it had another error suggesting that the table already existed and it was a fatal error.

An non-recoverable error happened during the update. Error details: CDbCommand failed to execute the SQL statement: SQLSTATE[42S01]: [Microsoft][ODBC Driver 11 for SQL Server][SQL Server]There is already an object named 'lime_notifications' in the database.. The SQL statement executed was: CREATE TABLE [lime_notifications] ( [id] int IDENTITY PRIMARY KEY NOT NULL, [entity] nvarchar(15) not null, [entity_id] int not null, [title] nvarchar(255) not null, [message] nvarchar(max) not null, [status] nvarchar(15) default 'new' NULL, [importance] int default 1 NULL, [display_class] nvarchar(31) default 'default' NULL, [created] datetime not null, [first_read] datetime null )

Our next attempt was to delete the table and continue.
the application then upgraded.

I believe there is something wrong in the upgrade db script. It checked for the existence of the table notifications and if not present, dies yet later on, it asked to create the table. Why was it looking for the notifications table if it was to be created later?
Perhaps I should not have upgraded 2.05 to Version 2.65.1+170522 directly.

I think it now works. I will see what happens for the next minor point upgrade.