public void contextInitialized(ServletContextEvent servletContextEvent) {
    thread = new Thread(new Runnable() {
      @Override
      public void run() {
        while (true) {
          try {
            Thread.sleep(2000);
            AsyncContext context;
            while ((context = queue.poll()) != null) {

  Future<String> result = lookupService.findPage();
        deferredResult.setResult(result.get());

public interface LookupService {
  public void findPage(DeferredResult<String> result) throws InterruptedException;
    
}

@Service("lookupService")
public class LookupServiceImpl implements LookupService {

    @Async
    @Override
    public void findPage(DeferredResult<String> result) throws InterruptedException {

        Thread.sleep(500);
        double r = Math.random();
        System.out.println("findPage" + r);
        if (r > 0.5) {
            throw new NullPointerException("test");
        }

        result.setResult(String.valueOf(Math.random()));
    }

@Controller
public class RestController {

    @Autowired
    FacadeLookupService facadeLookupService;
    
    @Autowired
    LookupService lookupService;

    @RequestMapping("/hellou")
    @ResponseBody
    public DeferredResult<String> hellou() throws InterruptedException, ExecutionException {
        DeferredResult<String> deferredResult = new DeferredResult<>();
        lookupService.findPage(deferredResult);
        return deferredResult;

    }

@ControllerAdvice
public class ExceptionHandlerController {
    
       
    @ExceptionHandler({InterruptedException.class,
        ExecutionException.class
    })
    ResponseEntity<String> handelConflicts(Exception e) {
        System.out.println("handelConflicts ");
        return new ResponseEntity<>(e.getMessage(), HttpStatus.INTERNAL_SERVER_ERROR);
    }
    
    
    @ExceptionHandler(Exception.class)
    ResponseEntity<String> handelException(Exception e) {
        return new ResponseEntity<>(e.toString(), HttpStatus.INTERNAL_SERVER_ERROR);
    }
}

чтобы была честная асинхронность - нужно просто засунуть в метод deferredResult

так : 
public interface LookupService {
  public void findPage(DeferredResult<String> result) throws InterruptedException;
    
}


@Service("lookupService")
public class LookupServiceImpl implements LookupService {

    @Async
    @Override
    public void findPage(DeferredResult<String> result) throws InterruptedException {

        Thread.sleep(500);
        double r = Math.random();
        System.out.println("findPage" + r);
        if (r > 0.5) {
            throw new NullPointerException("test");
        }

        result.setResult(String.valueOf(Math.random()));
    }


и тогда контроллер : 

@Controller
public class RestController {

    @Autowired
    FacadeLookupService facadeLookupService;
    
    @Autowired
    LookupService lookupService;

    @RequestMapping("/hellou")
    @ResponseBody
    public DeferredResult<String> hellou() throws InterruptedException, ExecutionException {
        DeferredResult<String> deferredResult = new DeferredResult<>();
        lookupService.findPage(deferredResult);
        return deferredResult;

    } 

 @Controller
public class RestController {

    @Autowired
    FacadeLookupService facadeLookupService;
    
    @Autowired
    LookupService lookupService;


....

    private final Queue<DeferredResult<String>> responseBodyQueue = new ConcurrentLinkedQueue<>();

    @RequestMapping("/hellom")
    @ResponseBody
    public DeferredResult<String> hellom() throws InterruptedException, ExecutionException {
        DeferredResult<String> deferredResult = new DeferredResult<>();
        responseBodyQueue.add(deferredResult);
        return deferredResult;
    }

    @Scheduled(fixedRate = 1000) //TODO  fixedDelay =  для 1 потока
    public void processQueues() throws InterruptedException, ExecutionException {
        System.out.println("processQueues :" + responseBodyQueue.size());
        for (DeferredResult<String> deferredResult : responseBodyQueue) {
            Future<String> result = lookupService.findPage();
            deferredResult.setResult(result.get());
            responseBodyQueue.remove(deferredResult);
        }
        
    }