You really can’t deal with flyaway hair in LR. You need to take it over to PS. There are a ton of ways to clean up hair. But for those images simple spot healing tool or clone stamp tool will clean them up nice and easy. As for the eyes. You can enhance the color in light room. But the color looks pretty good. The sharpening tool in photoshop works really good for making the eyes pop. If you are not familiar it is the triangle shape icon. Just pass it over her eyes a couple of time and it really makes a difference. You can also use it on the lips eyebrows and eyelashes when needed. Just don’t over do it. A pass or two is all you need. Have fun.

I think these are excellent. You did a great job with the lighting. Personally, I do not like images that are too soft and over processed, I think these are pretty spot on as far as that goes. You softened the face enough but didn’t over do it. Here are my two critiques. The eyes, her left facing camera eye has a bit of brown in it. Did you consider fixing that? Personally I would have sharpened the eyes a little to bring them out more. They have great color overall a little sharpening would have made them really “pop”. The second thing I see is with the pose in the second image in each set. While technically very good they are not a flattering as the first. She has a little bit of deer in the headlights look. Also because of the angle of her shoulders she appears “heavier”. A little bit more of an angle would be thinner for her as it is in the first image in each set. Lastly, and this is purely personal preference I would clean up some of the flyaway hair. On the right facing camera side there is a little more than I would like.
Overall you should be very happy with these. I know I would be if I had gotten this result. You also have to keep in mind we are all photographers so we are going to see every little imperfection. The client and everyone else looking at these is going to see amazing images. Well done.