Fwiw I've found the tethering in Lightroom unreliable with both 7100 and 800. I use digicam control to feed a Lightroom monitored folder.
I was a beta-tester for DigiCam - it's a great product but they don't make one for the Mac - so when I use it, I have to run VMware with Windows 7 and DigiCam. But that was the days of Lighroom 4 when the D7000 and D7100 was not support. Since LR 5, support for D7100 has been very solid and reliable - I shoot studio so it's always tethered.
One important thing that new tether shooters don't realize is that the little connector at the camera end is very finicky and cannot take any load - so just letting the cable hang can pull it out enough to lose connection. So, if you tether, never let the connector friction carry the weight of the cable - warp a thing velcro strip to the connect end of the cable and attach it to the camera strap ring to take the load off - then it's very reliable.
Oh, one more thing, if you upgraded recently to LR 5 or 5.3, make sure you go to the Plug-In manager and remove the tether plug-in and then add it back - that's how you get the new version in - the LR 4 (or earlier) versions don't support the D7100.