使用 Lambda 和互斥锁（Mutex）解决此问题，具体实现代码如下：

1. 创建互斥锁

var mutex = new Mutex();

2. 在 Lambda 函数中设置互斥锁

exports.handler = async function(event, context) {
    // 尝试锁定互斥锁
    if (!mutex.tryLock()) {
        console.log('Another execution is already processing the queue.');
        return;
    }
    try {
        // 处理队列消息
        await processSQSMessages();
    } finally {
        // 释放互斥锁
        mutex.unlock();
    }
};

3. 互斥锁实现代码

class Mutex {
  constructor() {
    this.locked = false;
    this.waiting = [];
  }

  tryLock() {
    if (!this.locked) {
      this.locked = true;
      return true;
    }
    return false;
  }

  async lock() {
      // 添加等待锁的进程
      this.waiting.push(new Promise(resolve => resolve()));
      // 等待许可
      await this.waiting[this.waiting.length - 1];
  }

  unlock() {
    // 解除锁
    this.locked = false;
    if (this.waiting.length > 0) {
      // 来自等待列表的进程许可
      const nextResolve = this.waiting.shift();
      nextResolve();
    }
  }
}