Right click (or click-and-hold) the Lightroom icon in the Dock and select “Options > Assign to” to configure Lightroom’s spaces behavior. It’s probably set for All Desktops. Switch to the desktop/space you want Lightroom to stay in, and select “Options > Assign to > This Desktop”.
Mark, I am amazed at how simple that was. Thank you so much! Works like a charm. Though I have been using Mac and lightroom for many years I have never had any application present like that. I was sure it was something to do with Lightroom. You are a wizard Mark. Incidentally this is the first time (at age 71) I have ever asked a question on any forum... and after this experience it wont be the last.
Glad to help. It may have been simple, but it was far from obvious. Most of the Mac users I know (and I've been using Macs since 1988), don't even know what spaces are, so you're way ahead of the curve.