Each installation of LPCXpresso , Red Suite and Red Suite (NXP Edition) is completely independent. Thus it is quite possible to install more than one version of any (or all) products at the same time - as long as you choose to a different installation directory for each installation.
This allows you, for example, to safely test out a new version of the tools, whilst having your previous version still available. And each version of the tools will automatically pick up the appropriate license/activation file. For license file details please see the FAQ "Where is my license file stored?"
Note that if you wish to test out a new version of the tools, you are advised to create a new workspace to do your testing in, rather than using your current workspace. Thus you will need to export any projects you wish to use in your tests from your current workspace, using the previous version of the tools, and then import them into the new workspace using the new version of the tools.