Cannot install Mac OS X Lion due to disk errors
If you were to purchase Lion from Apple, then a requirement to install would be to have Snow Leopard already installed. In other words, the DMG file only offers an upgrade to Lion. You probably can not use the DMG file to create a bootable installer. You can read the requirements from this Apple website.

You would not need a Apple ID to install Snow Leopard, but the installer will still ask. You can decline to give an Apple ID if you wish. Snow Leopard was released on a DL DVD. Apple still sells Snow Leopard DVDs, but you can also download an ISO from the internet. There are plenty of websites that explain how to make a bootable USB Snow Leopard installer. I have not tried any of these methods. If you succeed, then maybe you could post a method that works.


  I would recommend burning the Snow Leopard ISO file to a DL DVD.


Once you have Snow Leopard installed, you should install all the available Snow Leopard updates. This would update Snow Leopard to OS X 10.6.8. From here, you could upgrade to Lion by using your DMG file. Or, you could open Safari and search for the Apple website where you can download a free upgrade to El Capitan. 


  Note: You may need an Apple ID to download El Capitan. If so, then use an existing Apple ID or create a new ID. Apple does not charge for creating new Apple IDs