Yes, Lynn. LR is platform independent and will read it with no problem. I have a MacBook Pro and an IBM T41 laptop that I use in my presentations to show just that.
On the drive transfer...A portable product such as the WD MyPassport or MyBook drive works well, as it is readable on both platforms. I prefer to use the MyPassport style as it does not need an external power supply...jus the USB port. If you use a MyBook, you'll also need an extra outlet for power, and I highly recommend a UPS to go with it. Besides...the MyPassport drives slip right into my laptop case and are barely noticable weight/size wise.
Go get a fresh cup of joe and read on. There are options and right/not-so-right ways to do this, and I'd like to give you the benefit of the experience I've had learning to do this routinely (experience is the by product of making a ton of mistakes and often).
Just like in Photoshop, there are many ways to do something. The question is: are you planning on moving your LR work back and forth between the two machines? If so, you can set up LR to do that easily. Is this a one-way move from the PC to the Mac? If so, that's another school of thought. I say all this because how you approach this can make it easy or difficult to be bi-computerly (as I am).
Theory in practice: I move my LR between the two computers routinely. This allows me, as a professional photographer, to make use of any machine for editing or a presentation (LR IS GREAT for presenting to clients - the image elimination process is a dream using stars or colors) and if a computer crashes, I can still work.
To do this, I place my entire catalog, previews and content on the portable drive (that is backed up nightly). That way, I open LR on which ever computer, open the catalog and point the missing folder to the correct drive and I'm off and running.
If you're just moving your LR content in one direction, copy all the above mentioned to the portable hard drive and then copy it to the main drive on the Mac, and when you open that catalog on the Mac drive you're back at work.
Here's the easy way to re-find your images after the move (recommended). LR will give you gray images with question marks and digital bug boxes because it can't find the photos. Go to the Folders panel in Library module and find the HIGHEST level folder for the drive it was on. Control-click (or right click if you have a mouse) on it and select Find Missing Folder.
Navigate to that folder on your new drive or location on the Mac and select it and then select Choose. ALL your images will be found. This is the easy way.
The hard way (not recommended): Do the same procedure but on a sub-folder. I say this is the hard way because LR will find JUST that folder's images, and it looks no further. To find the rest of your images (which are still lost, as far as LR is concerned) you'll have to use this find function for EACH AND EVERY SUB FOLDER until they're all found. Not so efficient, I say.
I hope this helps. I know there's a lot here, but I've found there are hard ways and easy ways to do this.
Marty