Office 2008 uses a simpler encrypted license file which as far as I recall is not linked to a physical device, this file for Office 2008 is located in a sub-folder of the Office 2008 application folder and as long as it is copied keeps the license with the application.
Office 2011 however uses both a more complex encrypted license key and a key that is linked to a physical device, therefore even if you copy this file to the new Mac it will not be valid on the new Mac and it will detect this and force you to re-enter the license key. If you have lost the original key you will probably be forced to buy a new one. In the past for older versions of Office for Windows could get new keys generated by Microsoft but even there I believe this was only possible if you had the original media i.e. DVD with a code on it that they could verify. Microsoft never offered an equivalent service for Office 2011 for Mac and I know because I once was in the same situation and tried speaking to Microsoft about it.
Office 2016 is now the current version. If you buy a new copy you will kill two birds with one stone by replacing your lost license and getting an upgrade.
Remember it is not Microsoft's fault you lost the original key.
Note: If rather than moving to a new Mac you merely want to wipe and reinstall on your current Mac, or perhaps the hard drive died and you want to restore/migrate from a backup then as long as the Office 2011 license file is restored and it is the same Mac it should work. For Office 2011 the license file is in /Library/Preferences/com.microsoft.office.licensing.plist
