LR6 / CC2015 is not available in a 32Bit version, only 64Bit.
32Bit OS's limit RAM to 4GB (theoretically) and to 3GB (practically). There is no way around this border.
You can download every main x (x.y) version you like for Mac or Windows at no additional cost.
When you currently have a 32Bit version you seem not to be on the latest CC 2015. You may be using 2014 and you can update to the latest 2014 using the update functions or the usual downloads after a re-installation. You need a 64Bit OS to be able to update to the latest CC2015.
I like the part that the solution is downloadable at no extra cost, What i dislike is that the 32bit Versions of PS and LR actually dont work on Win10 32bit systems. But I gues that I have to upgrade.
They actually should work on W10 too. You need to make sure that W10 gets as much RAM as possible and that no other applications are running at the same time.
I'm not a Mac guy, so I don't know if there are any option in Bootcamp to adjust the amount of RAM W10 gets.
btw: I don't see any reason nowadays to use a 32Bit OS - I did not come across an application that did not run on 64Bit OS lately (in 32Bit Mode of course).