I did it!
The problem, as I suspected already, was in my antivirus (COMODO Internet Security).
The program lazarus.exe was registered in Defence+ Rules of COMODO as "Trusted application". That proved to be not sufficient, it must be "Windows system application". After that setting project1.exe can be rewritten without problems.
Thanks to everybody for brainstorming.
To justify my slowpoking I want to say that I have never met such behaviour of compilers before. For instance, Delphi and Borland Pascal work fine without such settings.
Upd: The said above is not true for all version of COMODO. In some cases, i.e., one must to switch off "Auto-Sandbox" option.