I don't know about lambda functions but I think you can do all of this with rsync.net since we have both s3cmd and git in our environment:

  ssh user@rsync.net s3cmd get s3://rsync/mscdex.exe

  ssh user@rsync.net "git clone git://github.com/freebsd/freebsd.git freebsd"

So you could run a cron job that would clone a repo to your rsync.net account and then publish (or backup) that repo to an s3 account.

Or whatever.