[Vuejs]-This request takes too long to process,

You can increase the php max execution time, but that is not a good approach unless is really needed.

Check the

storage/logs/laravel.log

To se what is the actual issue on the code, it might be a time out if that is the case try to see if you can do something in the code to be more efficient, If this is a report that might take long time to execute, you can also consider creating a command.