There is no kern lookup feature in InDesign and there never has been. InDesign either uses Metrics Kerning (built into the font) or Optical Kerning (using the shapes of the glyphs).
And you can manually kerning using the Kerning control on the Character and Control panels.
COntextual kerning was never a part of InDesign as it was with Quark Xpress.
But you can create a Character style and use it in a GREP Style or you can use Optial Kerining.
To be more specific?
The opentype “kern” positioning feature, that I use in the fonts I produce, uses class based and contextual positioning. This used to work in InDesign as late as before last update? This made it possible to add a contextual kern for difficult pairs like ”L’A” /L /apostrophe + /A) or abbreviations like ”S.P.Q.R” where as /P /period /Q get too close together, without the need for extra manual labour.
This is what the contextual kern feature looks like:
pos L' 60 [quotesingle.case uni2032.case quoteright.case quoteleft.case quotereversed.case] A;
pos L [quotesingle.case uni2032.case quoteright.case quoteleft.case quotereversed.case]' 210 A;
pos P' 150 [period comma] @CASE;
pos P [period comma]' 120 @CASE;
A shot in the dark: does your text by any chance apply the 'ital' OpenType feature and/or use Japanese?
Background info: Japanese fonts sometimes support 'ital' to choose italics within the latin script, and the OpenType feature is also supported with a matching InDesign text attribute, only accessible in Japanese UI.
Some years ago I wrote an InDesign plugin that allows to preview and explicitly invoke OpenType features. Back then I've observed that for an enabled 'ital' the composer (not sure which or all of them) would suppress the 'palt' and 'kern' features otherwise enabled by default (along with 'locl', 'rlig', 'mset', 'ccmp', 'mkmk' and 'mark'). Thus a stray italics text attribute (override or via style) could indeed disable the font's kerning.
To add to the confusion, the OpenType actually specifies the opposite "In CJKV fonts it should activate the kern feature (which would be on anyway in other scripts)", so the error could be on my side, but I just checked my code and back then I spent quite some time to get my preview composer match the real one. Thinking it over I also wonder about the technical conditions that trigger the "In CJKV fonts" precondition, I never got that far.
Anyway - Thomas, if you are interested to further investigate this or see interaction with other OpenType features, send me a direct message - I still occasionally build a Mac version of that plugin.