Lightroom is a database in the Catalog along with other tools.
Your PSE Organiser can be imported by Lightroom into a Lightroom Catalog. A copy will be made so the organiser will be left untouched.
Now how to do this?? I'm not sure....
I guess the Organiser being on the PC and with the way PSE works will be a PC only readable database??? Lightrooms are cross platform (work on either PC or Mac). So I am thinking that you may need to download Lightroom (just do a Trial) on the PC, create a new Lightroom catalog and import from PSE into that.
Then you can transfer the Lightroom Catalog to the new Mac.
There are questions of where you image files are as well.
Tell us a bit more where you have files - internal or external drives???