My Apple TV is off and I lost the remote and can’t trun on with my phone

You can choose to buy a replacement remote.

Identify your Apple TV remote - Apple Support

Remotes & Controllers - Apple TV Accessories - Apple Store

If you have an older Apple TV then you will need the physical remote in order to pair with the remote on your iPhone. Regardless of model it will require it to be on the same network as the iPhone, if not then that will also require the physical remote (or alternatively a restore and pair with BT keyboard to setup the connection).