The problem is with the font. Specifically the WinAscent setting.
LibreOffice uses this as the upper limit of any glyph.
You can see how this works by highlighting some of the text.
I ran into this recently when testing OpenType features such as stylistic sets.
You can see by the highlighting that those swashes are outside the box.
What is odd is that the zoom level affects the display.
At 150% (this image) you can see only the larger text looks correct.
At 200% nothing looks correct.
At 100% all looks correct.
I tried zooming on your font and it did not help.
Note that Word 2016 has the same issues.
I opened the font in FontCreator and took a look.
In the image below you can see where your characters are being cut-off at the WinAscent line.
More advanced applications do not have this issue.
Both fonts look fine in QuarkXPress. See image below.
Yesterday while testing font families I found a similar issue with a new font family.
Libre Franklin has been forked to become Public Sans.
The new developer adjusted the font metrics to “normalize” them.
This resulted in the descenders being cut-off of for example the lowercase “g” is what I noticed first.
Same issue on the bottom.
Not sure why your font was designed like this.
It is my understanding that there is no easy fix.
If this answers your question, please check the checkmark at left.
Not sure if this is just a LO on Windows issue.
Could some Linux and Mac users please test?
I got the font here:
WinAscent and WinDescent are only used by Windows.
They define the upper and lower limit of the glyph on Windows.
So since WinAscent on this font cuts right through the diacritics they appear cut-off.
Export to PDF uses a different rendering engine so it does not have this issue.