A conclusive answer can not be provided because that depends on what method was used to install Lazarus (and the Free Pascal compiler). E.g, compiled manually from source, FPCUpDeluxe, Zip-File from somewhere, Portable version, official installer (from where), package-manager (which one) etc..
edit: in basics (for a normal setup) there are two important files a) "lazarus.cfg" and b) fpc.cfg. Depending on the version of Lazarus file a might not be available/supported in which case the start parameter -pcp in the startup-link comes into play. The settings in there now refer to your current location where things are stored and these should be adjusted to match the new location. Other than that it is a simple move from the original location to the new location. Perhaps could trigger the Lazarus setup dialog (again depending on your version of Lazarus) for reconfiguration because it was unable yo locate the debugger, FPC compiler and/or other tools it depends on.
Whatever you do make at least a backup of all your FreePascal and Lazarus configuration directories/files.