This is the professional, safe, and fast way to achieve a portable workflow on macOS.
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. lightroom portable mac
Here is the truth about Lightroom and macOS portability. Yes, but not the way you think. This is the professional, safe, and fast way
You want to edit on an external drive. You want to travel light. You want speed. This is the professional
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.