Here is the truth about Lightroom and macOS portability. Yes, but not the way you think.
Instead, (approx $80). Install Lightroom Classic normally on your Mac (it has to live on your internal drive). But store only the Catalog and Photos on the external SSD. lightroom portable mac
You cannot install the application on a USB stick and run it on a stranger's Mac (macOS prevents this due to security certificates). However, you make your working environment portable. Here is the truth about Lightroom and macOS portability
This is the professional, safe, and fast way to achieve a portable workflow on macOS. lightroom portable mac