Thanks for your reply.
I wiil go with Thunderbolt drive enclosure, which I find as a good solution.
I want the upgrade as Lightroom is running too slow.
/Per
I would think, though, that to run any software on such an external drive, the Mac OS needs to be installed there. However, if the software you need to run faster is limited, ie, just Lightroom and one or two others, maybe you do not need such a large SSD drive. Maybe a 512 gig one would suffice.
What you can do is to use software like either SuperDuper! or Carbon Copy Cloner to make a copy/clone of your stuff that you have on the iMac. That will include the OS, and such a backup/clone will be bootable. You can then boot your iMac from that clone, and your iMac's drive would appear on the desktop of that "clone" environment. Given that you will have Thunderbolt connectivity, booting from such a clone, and running programs on it, should be fast. I have a Samsung 850 Pro 512 gig SSD enclosed in a nice, slim Orico enclosure, with USB 3.0 connectivity. I mainly use that drive for backing up each of my Macs with SuperDuper! each week, but even via USB 3.0, the performance is good.
Or, of course, you can just get that external SSD "ready", install the Mac OS onto it, and then install any software there. You can then boot your iMac to that device, and run Lightroom (and whatever else you want) from there.