Transfer to new computer

Are you trying to avoid using a slow download link, or a cell phone with limited data?  Unfortunately, you are going to have to install it via the Creative Cloud desktop app or it won't work.  That's 100%.  If you do have a very slow connection or limited data, then you can avoid having to download it a again by using the download links on ProDesignTools.

https://prodesigntools.com/adobe-direct-download-links.html

Alternatively you could find a local hotspot, or ask a friend with unlimited data.  If you are installing the Photography Plan apps, then that's going to be several Gb.

Migration tools often fail for inexplicable reasons. Hardware drivers, registry entries or software settings may be missed etc. Different people have different levels of success with them.

I've used them in the past with middling results. The process still took hours but not everything migrated 100% which left me less than confident with the end result. I now invest the time and clean install every time with 100% confidence.

Nothing to stop you trying but Adobe software traditionally does not migrate seamlessly. 

Most people who try it in these forums seem to end up having to do a clean install of their Adobe software.

It may or may not work, but even if it does, you risk having problems that may surface in the future.

I'm not familiar with Laplink, but I don't think so.

Install the Creative Cloud desktop app on the new computer, then use it to install PS and LrC.