Your question stem from API principles and not lumen vs
You have over-engineered this. As everyone has pointed out that there are many way to consume the API which is something that you failed to grasp.
In basic web design: you have data (unless you have a static page which has static data), then you have the html + css to render the webpage.
In Laravel your views are your html + css, and then you have Eloquent (or enter DB source like mongo, etc) that fetches data for you.
Now in API design (can be in any language) that fetching component just like Eloquent is where your API comes in. The API service is your data source and platform to serve your data.
Each platform / language has different way to consume the data that you have provided. Angular / Vue /jQuery are data binding frontend end platform. You can have a PHP application that in turn uses curl to call your API service (guzzle is a popular wrapper). You could have NodeJs as a servelet web application being your middleman that actively consume and communicate your data source.
As @jekinney and @Gog0 mentioned - Lumen is your delivery service for the API, now you need another application to consume it.
As others pointed out - you could import in views to the lumen, but then if you do that, you might as well have a full Laravel application. If your application holds both api + views - it maybe best to learn some frontend to abstract your backend (api service).
tutorials on the internet usually separate API from consuming it because it will depending on how you want to consume it. ie: a stripe API is for processing, where as google api can be for many types of services, etc.
Since you are new to this playing field: why dont you experiement with having two different PHP application as a starting ground rather than ask us for best way: 1 lumen api, and 1 plain php that just calls your end points and renders the data afterward and see the limitation. If it fits, maybe its good enough - then move towards frontend or utilize everything in one application.
Time is irrelevant because if we tell you to pair it with javascript you will spend time trying to understand javascript. So my suggestion for you is 1) understand what is an API and how to utilize it and why applications uses it 2) continue using PHP as your view rendering system by pairing it with any framework that renders PHP into HTML (laravel itself does it through blade) and self call your API.