@domas I had a similar problem and to fix this you need to:
Check your Laravel Application - consider refactoring and optimizing your code, install laravel-debugbar if you haven't already and you will see DB queries that you might not be needed and how fast/slow a page request is. Some common scenarios are, looping MySQL queries (also called n+1, search it), also loops that do some crazy calculations that can be refactored, etc.
Upgrade your server - We have set up a load balancer running 4 instances of the server so we can scale it up when needed. We made sure our routes/config/views is cache, we also use Redis as the cache, session, and queue driver instead of the typical file/database driver which is much slower.
TLDR, just upgrade your server setup or make time to optimize your Laravel application code.