RAW pictures on External Hard Disk Lightroom Classic/Photoshop on External Hard Disk

YorkHouse  wrote To reduce overfull memory on Mac Book Air Laptop I have moved Raw pictures to an External Hard Drive. I can find photos by clicking on Folders + then name of my Ext HD but I cannot process them in Library/ Develop because the screen changes  to Catalogue and asks me to add. I do not want to put the pictures back on Internal HD. I think many photographers keep pictures on External H D and process on Laptop. I will be grateful if anyone can advise me how to get from Ext H D to processing in Lightroom/Photoshop

Since you have manually moved the images after you did the Lightroom import, you need to tell LR where you moved the images to.

In the Library module, go to the Folders panel,

find the top-most folder with a "?" indicating that it is "missing",

right-click on it, select "find missing folder",

navigate to your external drive, select its new location.

Repeat as needed.

When you set up your initial Lightroom Catalog (or the Catalog connected with this issue), where did you choose to save the Catalog file?

This is important in the context of your question.

YorkHouse  wrote To reduce overfull memory on Mac Book Air Laptop I have moved Raw pictures to an External Hard Drive.

Do you mean hard disk space and not memory?

I can find photos by clicking on Folders + then name of my Ext HD but I cannot process them in Library/ Develop because the screen changes  to Catalogue and asks me to add. I do not want to put the pictures back on Internal HD.

If it is asking you to ADD, then you are doing it wrong. ADD happens in the Import dialog box, you do NOT want to import these photos again, you have already imported them.

Since you moved the photos to a different location, you need to tell Lightroom where they are. You do this in the Library Module, not in the Import dialog box. Please follow these instructions: Adobe Lightroom - Find moved or missing files and folders

I'm not sure I understand the question. (Double) clicking on an image in the Finder is not the way to edit an image in Lightroom Classic. That is not how Lightroom works. The images need to be imported in the catalog first (you can do that with images on an external disk too). That will not copy the images to the catalog, the catalog is like an address book. It only contains links to the images and metadata of the images. When you import the images, use 'ADD' at the top middle of the import dialog. That will make sure that Lightroom only adds the information to its catalog, and does not move or copy the images to another place. Maybe it's a good idea to get an instruction book about Lightroom Classic. The Lightroom Queen has a free starter guide: https://www.lightroomqueen.com/ 

If Lightroom starts when you double click an image, you'll have to change that in the Finder. An editor like Photoshop should start up in that case, not Lightroom.