Is your app to be the only thing running on https://www.clientdomain.com/ ?
Or does your client have a regular site and expects your app to run from a subfolder?
If your app is the only thing running on that domain, install it as it would be served from the root path, wrap your routes in a Route::group(...) and add /en/applicationname as a prefix. This should work.
If your app is not the only thing running in that domain, try clearing the app's routes cache.
php artisan route:cache
Unfortunately serving an app from a sub-path is not supported by Laravel.
There are a lot of issues open in Laravel's GitHub issue tracker regarding this setup. Most issues complain apps breaking after caching their routes, but there are issues with URL signing and other URL related tasks (URL generated in notifications/queues jobs, etc.).
The official instance from Laravel maintainers is that issues related to serving an app from a sub-path are not considered a bug.
From the docs:
https://laravel.com/docs/8.x/installation#directory-configuration
Laravel should always be served out of the root of the "web directory" configured for your web server. You should not attempt to serve a Laravel application out of a subdirectory of the "web directory".
Some GitHub issues related to this:
https://github.com/laravel/framework/issues/32236
https://github.com/laravel/framework/issues/32082
https://github.com/laravel/framework/issues/32832
https://github.com/laravel/framework/issues/34362
https://github.com/laravel/framework/issues/34977
https://github.com/laravel/framework/issues/35241
There are lot of arguments around saying a subdirectory in the domain is different then a subdirectory in the "root of the "web directory", but if you read through the issues you will see this is regarded as unsupported.
Clearing the route cache, as already suggested, seems to solve most use cases, but be aware other URL generation related problems can arise.
Hope it clears things up.