要在锁屏界面上显示AVPlayerLayer的控制器，你可以使用MPNowPlayingInfoCenter和MPRemoteCommandCenter来实现。下面是一个示例代码：

首先，导入相关的框架：

import AVKit
import MediaPlayer

然后，将下面的代码添加到你的AVPlayerViewController类中：

private var playerLayer: AVPlayerLayer?

override func viewDidAppear(_ animated: Bool) {
    super.viewDidAppear(animated)

    // 创建一个AVPlayerLayer并将其添加到view的层级中
    playerLayer = AVPlayerLayer(player: player)
    playerLayer?.frame = view.bounds
    view.layer.addSublayer(playerLayer!)

    // 设置锁屏控制
    setupRemoteTransportControls()
    setupNowPlayingInfo()
}

override func viewWillDisappear(_ animated: Bool) {
    super.viewWillDisappear(animated)

    // 移除AVPlayerLayer
    playerLayer?.removeFromSuperlayer()
    playerLayer = nil

    // 移除锁屏控制
    removeRemoteTransportControls()
    removeNowPlayingInfo()
}

private func setupRemoteTransportControls() {
    // 获取远程命令中心
    let commandCenter = MPRemoteCommandCenter.shared()

    // 设置播放按钮的响应事件
    commandCenter.playCommand.addTarget { [unowned self] event in
        if self.player.rate == 0.0 {
            self.player.play()
            return .success
        }
        return .commandFailed
    }

    // 设置暂停按钮的响应事件
    commandCenter.pauseCommand.addTarget { [unowned self] event in
        if self.player.rate == 1.0 {
            self.player.pause()
            return .success
        }
        return .commandFailed
    }

    // 设置快进按钮的响应事件
    commandCenter.seekForwardCommand.addTarget { [unowned self] event in
        if let event = event as? MPSkipIntervalCommandEvent {
            self.player.seek(to: CMTime(seconds: event.interval, preferredTimescale: 1))
            return .success
        }
        return .commandFailed
    }

    // 设置快退按钮的响应事件
    commandCenter.seekBackwardCommand.addTarget { [unowned self] event in
        if let event = event as? MPSkipIntervalCommandEvent {
            self.player.seek(to: CMTime(seconds: -event.interval, preferredTimescale: 1))
            return .success
        }
        return .commandFailed
    }
}

private func removeRemoteTransportControls() {
    let commandCenter = MPRemoteCommandCenter.shared()
    commandCenter.playCommand.removeTarget(nil)
    commandCenter.pauseCommand.removeTarget(nil)
    commandCenter.seekForwardCommand.removeTarget(nil)
    commandCenter.seekBackwardCommand.removeTarget(nil)
}

private func setupNowPlayingInfo() {
    // 设置当前播放音频的信息
    var nowPlayingInfo = [String: Any]()
    nowPlayingInfo[MPMediaItemPropertyTitle] = "音频标题"
    nowPlayingInfo[MPMediaItemPropertyArtist] = "艺术家"
    nowPlayingInfo[MPNowPlayingInfoPropertyPlaybackRate] = player.rate
    nowPlayingInfo[MPNowPlayingInfoPropertyElapsedPlaybackTime] = player.currentTime().seconds
    nowPlayingInfo[MPMediaItemPropertyPlaybackDuration] = player.currentItem?.asset.duration.seconds

    // 设置锁屏界面的封面图片
    if let image = UIImage(named: "cover") {
        nowPlayingInfo[MPMediaItemPropertyArtwork] = MPMediaItemArtwork(boundsSize: image.size) { _ in
            return image
        }
    }

    // 将信息设置到MPNowPlayingInfoCenter中
    MPNowPlayingInfoCenter.default().nowPlayingInfo = nowPlayingInfo
}

private func removeNowPlayingInfo() {
    MPNowPlayingInfoCenter.default().nowPlayingInfo = nil
}

这样，你就可以在锁屏界面上显示控制器，并且能够使用播放、暂停、快进和快退按钮来控制AVPlayer的播放了。请确保在使用这些代码之前，你已经创建了一个AVPlayer实例，并将其设置为AVPlayerViewController的player属性。另外，你也可以根据你的需求定制锁屏界面显示的信息，例如标题、艺术家和封面图片等。