You'd think that kerning would be the #1 thing to get right in a text processor, but LibreOffice shows me this:
Font is Palatino, with bold applied.
How to fix this? Note that the kerning is correct when I un-apply bold:
I must admit, I don't see the problem in your case, apart from a too narrow space, perhaps. But it could well be that the problem is just the on-screen display whereas print output looks correct. LibreOffice would just use the kerning tables from the font anyway and I guess it's very hard to get that wrong. Drawing glyphs to the screen in a pleasing manner is hard in contrast.
If when you toggle Pair Kerning in Format -> Character -> Position -> Spacing, then I'd have to say it was Xft-related. What LO version are you on?
If I recall, Libre Office uses Xft settings. I've had text rendering issues with certain version of libxft, so it may be worth rolling back to an older version if it's been updated recently.
Otherwise, have you made any recent changes to .Xresources?