Without knowing more about the app & the code, I can only speculate about reasons.
Potential reason #1: development mode.
If you are running ArangoDB in development mode, then the init procedure is run for each Foxx route request, making precalculation of values useless. You can spot whether or not you're running in development mode by inspecting the arangod logs. If you are in development mode, there will be a log message about that.
Potential reason #2: JavaScript variables are per thread
You can run ArangoDB and thus Foxx with multiple threads, each having thread-local JavaScript variables. If you issue a request to a Foxx route, then the server will pick a random thread to answer the request. If the JavaScript variable is still empty in this thread, it may need to be populated first (this will be your init call). For the next request, again a random thread will be picked for execution. If the JavaScript variable is already populated in this thread, then the response will be fast. If the variable needs to be populated, then response will be slow.
After a few requests (at least as many as configured in --server.threads startup option), the JavaScript variables in each thread should have been initialized and the response times should be the same.