Hi @LFirmiano,
Why do you think AdminLTE 3 is not able to work with CakePHP 4? Any theme can be used with any of the CakePHP framework. Please refer this https://book.cakephp.org/4/en/views.html on how views work in CakePHP.
Start by copying your theme’s css/sass files into webroot/css directory and call it into layout files, then see if it works.
Please share any particular issue here if you encounter any issue.