Yes, but it's really GPLv2 with the classpath exception [1] which makes it similar to the LGPLv2. Amazon's OpenJDK still has to be GPL. However, software using the OpenJDK can be licensed however you want (because of the classpath exception) [2].
Well Harmony was a JDK released under a more permissive license (Apache) but it has been discontinued. Moreso, unless you want to deal with being sued by Oracle and proving in court that your use of the JDK APIs are fair use (like Google had to do for Android), you really want to use something that is derived from OpenJDK, and thus GPL. So a more permissive implementation isn't likely to ever exist due to the legal liabilities.
[1]: https://openjdk.java.net/legal/gplv2+ce.html
[2]: https://softwareengineering.stackexchange.com/q/119436/69573