Unfortunately it appears that LibreOffice does not yet present an eyedropper button for in the toolbar, even though the eyedropper functionality is already present in LibreOffice. There is a way to do it, if you really want it … but in my opinion it would be better to install an external eyedropper program and examine your color pixels from there…
Here it goes:
1) Open LibreOffice Draw,
2) Select the menu "Tools : Color Replacer",
3) in the dialog that pops up, click on the small "Pipette" (eyedropper) button,
4) Move the mouse pointer to the pixel that you want to examine, and click to select it,
5) Back in the Color Replacer dialog, click on the first of the 4 "Source Color" boxes, and press the <SPACE> key.
6) There in the ColorPicker dialog that pops up, you can read out the color values of the pixel that you clicked.
( BTW, the 4 “Source Color” boxes are not working properly. )