Replay Manager, currently abandoned
When used with an open LeagueClient it will tap into its API
A "Match History" tab will appear and when you click refresh then it will list all the matches in the last 30 days and even let you copy the .rofl download url to your clipboard.

You are able to download replays from prior patches but you will not be able to play them without a client also on that patch

It can also launch replays from the replay folder which is specified in the LeagueClient Settings

Click Here