The lambda execution is not suspending and the lambda container has no port exposed when running a java 11 lambda with the latest localstack docker image by docker-compose with the environment variable LAMBDA_JAVA_OPTS=-agentlib:jdwp=transport=dt_socket,server=y,suspend=y,address=_debug_port_
    
It works fine for java8 runtime executions.

Docker command:

> localstack_1  | 2020-01-26T12:42:04:INFO:localstack.services.awslambda.lambda_executors: Running lambda cmd: CONTAINER_ID="$(docker create -i   -e ENV="$ENV" -e DOCKER_LAMBDA_USE_STDIN="$DOCKER_LAMBDA_USE_STDIN" -e HOSTNAME="$HOSTNAME" -e LOCALSTACK_HOSTNAME="$LOCALSTACK_HOSTNAME" -e AWS_LAMBDA_FUNCTION_TIMEOUT="$AWS_LAMBDA_FUNCTION_TIMEOUT" -e AWS_LAMBDA_FUNCTION_NAME="$AWS_LAMBDA_FUNCTION_NAME" -e AWS_LAMBDA_FUNCTION_VERSION="$AWS_LAMBDA_FUNCTION_VERSION" -e AWS_LAMBDA_FUNCTION_INVOKED_ARN="$AWS_LAMBDA_FUNCTION_INVOKED_ARN"  --rm "lambci/lambda:java11" "com.XXX.XXX.Handler")";docker cp "/tmp/localstack/zipfile.0c90736c/." "$CONTAINER_ID:/var/task"; docker start -ai "$CONTAINER_ID";

I think this is due to the fact that the classpath arguments and java opts are only being set if the rutime is equal to LAMBDA_RUNTIME_JAVA8 (line 211 of ocalstack/localstack/services/awslambda/lambda_executors.py , commit 03c6f4bf250edd18eb818ed65090f508636b0bff)
"""
        Return the Java classpath, using the parent folder of the
        given archive as the base folder.
        The result contains any *.jar files in the base folder, as
        well as any JAR files in the "lib/*" subfolder living
        alongside the supplied java archive (.jar or .zip).
        :param archive: an absolute path to a .jar or .zip Java archive
        :return: the Java classpath, relative to the base dir of "archive"
        """
        entries = ['.']
        base_dir = os.path.dirname(archive)
        for pattern in ['%s/*.jar', '%s/lib/*.jar', '%s/*.zip']:
            for entry in glob.glob(pattern % base_dir):
                if os.path.realpath(archive) != os.path.realpath(entry):
                    entries.append(os.path.relpath(entry, base_dir))
        
        
        entries.append(os.path.relpath(archive, base_dir))
        result = ':'.join(entries)
        return result
EXECUTOR_LOCAL = LambdaExecutorLocal()
EXECUTOR_CONTAINERS_SEPARATE = LambdaExecutorSeparateContainers()
EXECUTOR_CONTAINERS_REUSE = LambdaExecutorReuseContainers()
DEFAULT_EXECUTOR = EXECUTOR_CONTAINERS_SEPARATE
AVAILABLE_EXECUTORS = {
    'local': EXECUTOR_LOCAL,
    'docker': EXECUTOR_CONTAINERS_SEPARATE,
    'docker-reuse': EXECUTOR_CONTAINERS_REUSE
}