Let me assume first that the behaviour of a label with Anchors = [akLeft, akTop], Alignment = taRightJustify and AutoSize = true growing to the left when its caption is changed, is correct although it is not logical. I want to simplify the test project in order to understand what's going on - 18 labes is way too much...
The attached project contains a label with Anchors = [akLeft, akTop], Alignment = taRightJustify and AutoSize = true. I had dragged it to the very right of the form such that its right side aligns approximately with the right side of the form. While typing some text into the Caption property it can be seen that the right side of the label is held fixed and the label grows to the left. For the test I chose a rather narrow text for the label, e.g. '1'. And most of all, the label's Visible property has been set to false. In order to get around the mysteries happending during the OnShow/OnActivate events, I added a button which sets the label's Caption to a long text in the OnClick event and then sets Visible to true in order to show the label.
procedure TForm1.Button1Click(Sender: TObject);
begin
Label1.Caption := 'This is a long, long, long text.';
Label1.Visible := true;
end;
Running this and clicking the button, you see that the text changes, but it stays at its original starting position. Due to the special treatment of Alignment = taRightJustify it should have moved to the left so that it ends at the right edge of the form.
I think this is the problem reported.
I compiled with Laz/main and with Laz 1.4.4 (the oldest Lazarus that I still have), and both show the same behaviour. Therefore, it is not a recently introduced regression, and probably exists since the beginning. I also converted the project to Delphi, and here the behaviour is "correct" in the sense that the text ends at the right side of the form.
One other experiment with the Laz/version: Exchange the two instructions in the ButtonClick handler so that the label is visible when its Caption is changed. - Now the behaviour is like in Delphi. It seems to be essential that the label is visible.
Following the debugger shows that the issue occurs in TControl.AdjustSize which executes the autosizing operation (due to the changed caption text) only when the control and all its parents are visible.
Please file a bug report. Maybe a developer picks it up and attempts to fix it (but I hope that this will not happen because the autosizing code is very complex, and in my experience it is very probably that something else will break...)
Even if this is not fixed, you always have the possibility to set the label Anchors to [akRight, akTop] (rather than [akLeft, akTop]), and the right alignment will always work. Of course, now the label will move when the size of the container changes. If you don't want this you can put the labels into a panel without akRight (or use the anchor editor to anchor them to other controls).