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)
@app.route('%s/functions/<function>/versions' % PATH_ROOT, methods=['GET'])
def list_versions(function):
    arn = func_arn(function)
    if arn not in arn_to_lambda:
        return not_found_error(arn)
    return jsonify({'Versions': do_list_versions(arn)})
@app.route('%s/functions/<function>/aliases' % PATH_ROOT, methods=['POST'])
def create_alias(function):
    arn = func_arn(function)
    if arn not in arn_to_lambda:
        return not_found_error(arn)
    data = json.loads(request.data)
    alias = data.get('Name')
    if alias in arn_to_lambda.get(arn).aliases:
        return error_response('Alias already exists: %s' % arn + ':' + alias, 404,
                              error_type='ResourceConflictException')
    version = data.get('FunctionVersion')
    description = data.get('Description')
    return jsonify(do_update_alias(arn, alias, version, description))
@app.route('%s/functions/<function>/aliases/<name>' % PATH_ROOT, methods=['PUT'])
def update_alias(function, name):
    arn = func_arn(function)
    if arn not in arn_to_lambda:
        return not_found_error(arn)
    if name not in arn_to_lambda.get(arn).aliases:
        return not_found_error(msg='Alias not found: %s:%s' % (arn, name))
    current_alias = arn_to_lambda.get(arn).aliases.get(name)
    data = json.loads(request.data)
    version = data.get('FunctionVersion') or current_alias.get('FunctionVersion')
    description = data.get('Description') or current_alias.get('Description')