Yes.  Sure you can run Laravel projects on N99panel.
In Laravel, the exposed public directory is project_folder/public . If your Laravel project directly runs on the domain name, then under N99panel's website/VHost management interface, you would need to extend the root dir for which you would need to place public under the requisite field/option of root dir extension.
In-case you are running Laravel into a sub-folder like example.com/myproject , in that case you would need to use the url-alias functionality of N99panel.
Also you would very likely need PHP and composer commands in the SSH terminal. In order to use this functionality, please enable Full SSHD flavor under Manage SSHd/Crond, for the respective user. Now relevant PHP interpreter is available in the form of phpXX where XX is the PHP version. For PHP 7.4, it would be php74 and similarly for PHP 8.1, it would be php81 . Similarly for composer 7.4 (which uses PHP 7.4) is usable via composer74 and composer 8.1 (which uses PHP 8.1) is available as composer81 .