By render, I am assuming you mean convert RAW, with edits, via 'Export' in Lightroom. I am not assuming you mean creating previews.
- The simplest thing to do is to get an external hard drive.
- Format the drive in ExFat, so that both Windows and Mac can read and write to it.
- Copy all images, and Lightroom catalogs to this hard drive.
- Mount this drive to your Mac, launch the LR catalog from the external
drive, and edit your images.
- Create a Smart Collection or use Quick Collection to tag those images that you wish to Export.
- When you are done editing, simply unmount the drive. Plug drive into
your Windows machine.
- Launch Windows Lightroom from the
same external catalog, choose your Quick Collection, and click
'Export', letting the quicker Windows machine do the rendering.
I have had good success using a Network attached drive, where you can store your images and your LR catalog, which for you means no plugging or unplugging. And if you use a NAS, you don't have to worry about format either. However, its best to quit LR on one machine before you start it on another, to avoid corrupting your files.
Edit: LR and Network Drive or NAS...LR can work fine over networked drives, however, LR does not support multiple users, or multiple access. It can't lock a file in use, which means that if you use a network drive, and ever have LR open on one machine, and try to open it on a different machine, you will most likely corrupt your LR catalog. This is likely the primary reason that Adobe doesn't support this method: because they do not have the features needed to support his type of access safely. However, if you are careful, it works: simply be sure to ALWAYS close LR when you are finished and NEVER launch LR without checking the other machine first.
I have successfully used this over a WD MyBookLive (NAS) drive (slow), and I currently run my USB external drive attached to my router, as a networked drive (not-NAS), running LR on a Mac, and on a Windows machine. I do this for convenience, not the use case you are seeking. The Mac is my main photo editing machine, but occasionally I need an image while on the PC.