Sophie Vandenbussche schrieb:

I am looking for a way to add a header on the pages of a book or report class.

Select "headings" or "fancy" as page layout in the document settings menu.
Headings should be what you want, to be able to customize the headings, use fancy and have a look at the fancyhdr manual to see how the customization is done:
http://www.ctan.org/get/macros/latex/contrib/fancyhdr/fancyhdr.pdf

More precisely, I would like to have at the top of each page the title of the corresponding part of the document (except on the page where the title of the part is written of course, and except at the beginning of the document before the Part I begins)

The default headings should suit your needs. When not, you can turn off/on the headings using the commands
\thispagestyle{plain}
or
\thispagestyle{headings}
respectively in ERT.

You can also use the command
\pagetyle{}

regards Uwe

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