In Lyx, how to change "Part I" with some other text

LyX just provides an interface (or front end) to LaTeX. So, while you may see

Part I  Some text

as your title inside the editor view, the LaTeX code associated with it

\part{Some text}

will output

Experiment I  Some text

if you add

\renewcommand{\partname}{Experiment}

to your preamble (Document > Settings... > LaTeX Preamble). If you wish to change this in the editor as well (so the visual matches the PDF output), you need to edit the stdsections.inc layout file; specifically the part style:

Style Part
  Category               Section
  Margin                 Dynamic
  LabelString            "Part \thepart"
  LabelType              Counter
  ...

You would have to update LabelString to read "Experiment \thepart" instead.