Unfortunately, Final Cut Express HD was discontinued 7 years ago (June 2011) just before the release of OS X Lion (10.7). At that time the final FCE Update Release was v. 4.0.1 which is also now no longer available from Apple.
Apple released Final Cut Pro X in June 2011 upon the end-of-life of FCE-HD and original FCPro. FCP-X is Apple's current video editing application (in addition to iMovie).
Bottom line, there was never any guarantee that FCE-HD would run on Lion (10.7) or any later version of OS X/macOS. And there was always going come a day when FCE-HD would simply no longer be compatible with some new release of macOS. That day has probably arrived with Mojave.
If you had FCE-HD running successfully on High Sierra (or whatever version of macOS you were running before you upgraded to Mojave), I suggest re-installing that older version of macOS + FCE-HD on an external hard drive and booting from that drive when you want to run FCE-HD.