Can I install Lightroom on a new computer later?

correction/clarification to @John Waller's comment ,

you can install the cc desktop app from here https://creative.adobe.com/products/creative-cloud on as many computers as you own and use it to install all (or some, if you want) of your cc subscription programs.

the only (insignificant for internet connect computers) limitation is that you can sign-in (and therefore start your adobe programs) on, at most, two computers at any one time. because you can sign out from either (or both) signed-in computers using a 3rd computer, this could not (imo) be easier.

Yes.

You're actually permitted to have up to two instances of Lightroom activated at any one time, provided you only use them one at a time. So you can install and activate on your new computer without affecting the old computer.