You can't drop the Lion installer dmg nor a cloned dmg onto the "create a new virtual machine" dialog. Neither of those are bootable and that's why you aren't seeing anything boot. 

Apple in its infinite wisdom did not create a bootable installer for Lion. It only gave you a .dmg with an Installer package that you had to then run to install "Install Mac OS X Lion.app" into your Applications folder.

Further complicating things, if you are running a later Mac, Apple again in its infinite wisdom refused to let you install the "Install Mac OS X Lion.app" from the .dmg, saying that the application can not run on your computer.

I've found a way to get that installer App courtesy of Mr. Macintosh (https://mrmacintosh.com). One of the tools he recommends to obtain macOS installation media is an open source utility Mist (macOS Installer Super Tool - https://github.com/ninxsoft/Mist ). This is a tool that runs on Monterey and later. It provides a nice GUI interface to download macOS installers as far back as 10.7.5 - even on Macs that can't run them.

I just used it to download and extract the Lion installer app and then dragged/dropped the resulting installer app onto the Fusion Create a new virtual Machine dialog. The VM booted to the OS X Lion installer.