Log aws lambda handler exceptions with log4j2 using aws-lambda-java-log4j2

I'm using the official aws-lambda-java-log4j2, suggested here in a java lambda. I've noticed that uncaught exceptions are not logged with the root logger. For instance this lambda logs "handler" with log4j2 but not the thrown exception:

private static final logger = LogManager.getLogger();
public void handler() {
  log.info("handler");
  throw new RuntimeException("error")
}

The logs for an invocation of this function include the log4j2 info message, but the exception is logged plainly, without requestid, timestamp, or ERROR marker.

2019-10-07 11:39:02 43db1f36-0570-4b58-adc6-5c92ea62a862 INFO Example - handler
java.lang.RuntimeException: error
    at Test.main(Test.java:3)

It's harder to find exceptions in logs because you can't grep for the request id or ERROR.

Is there a common pattern to emit logs using the log4j2 root logger in lambda?

I don't want to wrap my handlers with try-catch-log-rethrow.

try {
  ...
} catch (Throwable t) {
  log.fatal(t);
  throw t;
}