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There are 3 packages for entering tablenotes in longtable: threeparttable, threeparttablex, and ctable. All these packages require entering latex code. It seems that the threeparttablex do not require entering code (exluding references to the notes) inside the table environment.
I tried (in TeX code ...

I made a full installation of the TexLive, and it's not working. I think it's not recognizing the new latex installation. how do I solve this problem?

it give nothing (not error nor information)

How do I install the Greek support file?
I made a full installation of the tex-live on my computer (Linux Ubuntu). How can I verify that Lyx is using this installation (at the university, I installed the Lyx on windows, and worked with no additional considurations).

while running latex i received the error: Font LGR/cmr/m/n/10.95=grmn1095 at 10.95pt not loadable: Metric (TFM) file no
and a description: ...e the film thickness was 30~\textgreek{m} m
I wasn't able to read the size data for this font,
so I will ignore the font specification.
[Wizards can fix TFM ...

Solved it. If you have the same problem the solution is:
1. make the table longtable
2. choose the first cell and enter setting
3. mark the header
4. add the number of lines necessitate for the heading
in this way, the \endhead command will appear after all the lines of the heading.

My header for longtable is composed of 3 lines (the upper contain merged cells for topic aggregation). When a line is marked as header, only this line become a header. How do I make the first 3 lines a header (to appear in the next page too).
Why a long table over several pages appear in the list of ...

This didn't work. The \pagestyle{empty} just change the headings, not the numbering, which continue to appear in the same manner.

Can I use in order to have no page numbering on the first page?

Insert Label (by menu item or icon) in the figure caption. Name it. In the place where you want to refer the figure, insert cross-reference (by menu item or icon). Select the label name you just entered.

That's all