Lightroom 6 is NOT Classic. IF your MacBook is running Catalina or newer it will not be possible to install Lightroom 6. Even though the program is 64-bit, the installer is 32-bit and will not run on the new operating systems. What operating system is running on the new MacBook?
If, however, you are using an older operating system then here are excellent instructions on how to move everything to the new computer. It's important that you follow instructions closely and not leave out any step.