In the Lumen 5.7 repo, the composer.json shows the below for PHP:
"php": "^7.1.3",
And per the Composer Version Constraints below, I would think PHP 7.4 should be compatible:
The ^ operator behaves very similarly but it sticks closer to semantic versioning, and will always allow non-breaking updates. For example ^1.2.3 is equivalent to >=1.2.3 <2.0.0 as none of the releases until 2.0 should break backwards compatibility. For pre-1.0 versions it also acts with safety in mind and treats ^0.3 as >=0.3.0 <0.4.0.
The Lumen 6.x GitHub repr shows the below in its composer.json file. So one would think that upgrading to this version would not be of much help in your scenario.
"php": "^7.2",
If you didn't already, I suggest running through all of the common update pitfalls, i.e. composer dump-autoload etc. and see if that's the issue at hand.