If you’re struggling to get a Google API key; there’s extensive information in the FAQ on the why, what & how. WP YouTube Lyte will automatically fall back to the old anonymous API v2 if you don’t provide a key. As API v2 will continue to work for a couple of more weeks, all will be fine. I am, in the mean time, working on a separate plugin that will automatically provide an API key for WP YouTube Lyte to use (and which in the future might offer other extra’s). You can contact me if you would be interested in test-driving that service-plugin.
Create and operate a proxy application that sits between the v3 API and each and every WP YouTube Lyte instance, taking care of authentication with an API key. Risk: having to write & install that proxy application, making sure it is available 24/7 (it’s a single point of failure) + obviously the same abuse-risk as in (2).