I have copied this post from a comment that I wrote else-LJ where someone was asking about the facility to add like buttons to posts and so on:

I had a spare couple of minutes and there was a new LJ release email in my inbox and so I found it for you by looking at previous release posts in lj_releases (which is worth watching for just these reasons).

The <lj-like> tag is mentioned in release #93 from June 19 2012.

The lj-like FAQ page.

Enjoy! *smiles*