The problem is the current version of the older macOS 10.7 to 10.8 installers is they have been repackaged into a .pkg file that must be run to extract & build the actual macOS Lion installer app and that requires using a working Mac compatible with Lion. I have not seen anyone being successful using any method of creating a bootable USB installer from these newer packaged installers for 10.7 or 10.8.
Unfortunately the various DMG archives found within these older installers (including 10.10 to 10.12) are not enough to make a bootable installer (unlike the later versions 10.13+ where the BaseSystem.dmg can be used to make a bootable recovery USB stick...to simulate recovery mode).
Some years ago when Apple changed the packaging of the older installers and allowed them to be downloaded from outside the App Store, I had found instructions for manually extracting & creating a bootable macOS 10.11 El Capitan USB installer. It was a lot of work (directions were not entirely clear), but it worked. However, a year or to later Apple changed the packaging slightly where those directions no longer worked, although a slight modification would allow one to be created although it was not identical to the official method (or even the older method)...the OS install was a bit different). I only went through it because I did not have a compatible Mac at the time to use & only had a Linux system or newer incompatible Mac. I never tried it with the 10.7 or 10.8 installers, although I think they were a bit different anyway at the time.
I don't think the BaseSystem.dmg is enough on those older installers to even allow it to simulate recovery mode and even if it does, then you still need to contend with Apple's mostly broken nature of Recovery Mode for those older systems & installers. I guess you can try using Disk Utility to Restore the BaseSystem.dmg file to a USB stick. I don't recall if the USB stick had to be MBR or GUID, but I believe it needed MacOS Extended (Journaled) file system (only a requirement of Disk Utility since the Restore would wipe out the file system).
If your target Mac is compatible with OS X 10.6 Snow Leopard, then start by installing that from DVD. Then you can just upgrade normally to 10.7. It would actually be better to just stay on 10.6 if that Mac is compatible since macOS 10.7 Lion had a very bad vulnerability that was never patched....my organization forbid us to ever use Lion again (the only macOS that we were forbidden to use).
Otherwise you are going to have to do a lot of research & get very creative to make a bootable Lion USB installer.