welcome to the forums!
macOS Lion (10.7) is 8 years old and quite a lot of things did happen in the OS. It’s a herculean task to stay backward compatible with old OS versions like this one and support must be dropped from time to time. balenaEtcher is based on the Electron, which requires macOS 10.10+.
Only 64bit binaries are provided for macOS, and the minimum macOS version supported is macOS 10.10 (Yosemite).
Source. This information is also mentioned in the Supported Operating Systems section.
What you can probably do is to browse the GitHub tags - every tag has attachments = release files (
.dmg for macOS). You can try to download older version and try it. Changelog can be useful. I’d start with the 1.0.0. If it works, you can try newer one, etc.
It doesn’t mean there’s a version which works with the macOS Lion. There’s a big chance that even 1.0.0 doesn’t work with it.
Maybe @zvin can help here. I mean, which tag / version to try. And if macOS Lion (10.7) was ever supported.