I suppose this is addressed to Michael, but I have several perspectives on it, so Ill contribute regardless.
1) I haven't done tests to see whether it makes a difference to results whether one Capture sharpens before or aftert doing LCE, BUT that said:
2) regardless of the order in which they are done, one needs to be careful because both processes (and there are variants in how LCE is performed) involve creating halos and if either were overdone in relation to the other, the image can emerge looking too brittle. The way to avoid this, regardless of processing order, is to do each on separate layers (automatic with PK) so that the opacity of each effect can be adjusted to taste.
3) Within Lightroom, you have the option to effectively do both at the same time and let the program sort out the processing order, which it does very well - by that I mean using the Clarity slider and perhaps Vibrance to achieve the effects of LCE, and the capture sharpening in the detail tab. You can (and should) examine the image at 100% to see the total effect, and you can work back and forth between them, leaving LR to optimize the processing order under-the-hood once the image is exported to PS.
Mark