Checked, the problem is a mixed use of new line sequences, TWebMemo.Text uses the Web standard Unix/Linux #10 as new line, TStrings class uses the Windows sequence: #13#10.
All text from the web/browser asigned to a TString class or descendant is handled like a single line !!
Any code related with TStrings failed !!
The line of code added fix the particular case of the previous sample:
WebMemo1.Text := StringReplace(WebMemo1.Text, #10, #13#10, [rfReplaceAll]);
procedure TForm1.WebButton1Click(Sender: TObject);
begin
WebMemo1.Text := StringReplace(WebMemo1.Text, #10, #13#10, [rfReplaceAll]);
WebMemo2.Lines.Add(format('[ %d ] Lines. Text:', [WebMemo1.Lines.Count]));
WebMemo2.Lines.Add(WebMemo1.Text);
WebMemo2.Lines.Add('');
end;