If lookpopup is showing and if user key press tab key, screen active control is being TListBoxTab. But listboxtab is not visible control, it is not using in advlisteditor.
constructor TAdvEdit.Create(AOwner: TComponent);
.....
.....
begin
.....
.....
if not (csDesigning in ComponentState) then
begin
.....
begin
.....
with FLookupListBox do
begin
begin
.....
TabStop := true; <- this line problem