Lightroom 6 is working with both of those operating system. As you have suggested, Lightroom 6 is 64-bit only. With El Capitan & the latest update, tethering of Nikon and Canon cameras is currently not supported. It is an issue that is being worked on. So it's probably best to stay with 6.1 or 6.2 if tethering is something that you require.
Yes , Lightroom 6 will work fine with Mac OS 10.10 and 10.11 except you can face some known issues as mentioned below.
System Requirements : System requirements for Adobe Lightroom for Mac and Windows OS
Some Known issue with El Capitan and Lightroom: Lightroom and El Capitan | Mac OS 10.11