How can I wake up a MacBook with lid closed? How can I wake up my MacBook pro with an iPhone, when the lid closed (no external display)?
MacBook is not connected to power and there's a local wifi that it can connect to.
macOS Sierra, has an option in Energy Saver > Power Adapter to "Wake for Wi-Fi network access." In earlier versions that option was in Network preferences.

Apple Remote Access will wake a Mac this way but I am unaware of any iOS app that does this.

Generally speaking Wake On LAN (WOL) requires the sending device to send a so called "Magic Packet" and the receiving computer to be able to receive it and act upon it. I believe that Apple supports this method of WOL but I have not tested it in quite a while.

So your job will be to find an iOS app that provides WOL capability as it should do what you are looking for.