In order to use LUT files in Photoshop you need Photoshop version CS6 or any Photoshop CC version. Photoshop supports LUT presets with format .3dl, .cube and .look. Lutmix offers LUT files in a variety of formats including: Cube, 3DL, CSP, PNG and LUT
Newer versions of Lightroom can benefit from the use of LUT files with format 3DL and CUBE but you need Lightroom Classic 7.3 or newer. In order to check your current version you have to open Lightroom and go to the top menu, click Ligthtroom Classic and choose About Ligtroom Classic and a small window like the image below will open. If your version is 7.3 or higher, you will be able to use LUT files in Lightroom.