I don't know why this is happening, but I can replicate your results.
Somewhere InDesign has a setting that doesn't want L*a*b colors and is converting them to CMYK. But this is only for spot colors.
Now, if you are truly using spot colors, then it doesn't matter if the swatch is defined as CMYK or L*a*b. It is the spot color ink that decides what it will look like.
However, if you aren't using spot colors, then change that designation in Illustrator to process.
InDesign won't convert the colors at all.
Hi there - I'm having the same issue – any luck with a fix?
The Pantone solid spot color libraries are now always defined as Lab. If you want Pantone's CMYK simulations use the new Pantone+ Bridge libraries