Have you looked at JupyterLab’s workspaces? See #3 listed here.
Normally, this demo opens with side-by-side related windows like you seek.
However, right now there is an issue that they don’t seem to work, see here. This older demo still works like it is supposed to so you can get a feel for how things should be working. (The docker container it works with may have built a long time ago with the older components in place.) Hopefully, workspaces will be fixed soon as others have pointed out among the linked issues for doing demonstrations, arranging windows the right way open opening is kind of important.
UPDATE: Maybe workspaces work via MyBinder sessions if you try on a fresh machine or in fresh browser? See discussion going forward from here. But maybe are in JupyterLab 3 or specific versions of JupyterLab 3? There is a caveat about the current ‘Try Jupyter’ JupyterLab example not working with the work-around or solutions that have worked elsewhere to resemble a fresh launch, see the ‘Caveat’ description here, which may suggest it is JupyterLab 3 or specific versions of JupyterLab 3 that do indeed have workspace issues.