As far as I know it is not possible to maintain seamless compatibility with multiple versions. Once you import a project into a new version, going backwards is not supported and can cause problems.
However, I would go a step farther and say that this is probably not desirable anyway. Because each LTS revision is essentially a different code base, behavior between revisions will be slightly different. This can lead to one developer coding something that doesn't work quite the same in another developer's release, or QA assigning a bug to a developer who can't reproduce it. Having everyone on the same release prevents this kind of confusion.
As for how to manage versions, it is really up to you how often to update, but at a minimum I would recommend researching and testing any new version before committing to it. I generally don't update very often unless there's something specific I want from the new version. At some point prior to release, you will probably want to lock down the Unity version to avoid any last-minute engine-related issues.