I was actually in your position a few months ago - a client had no budget to do a full on replacement of a six-year old system written in Drupal 7, but it was in dire need of some performance gains - i knew we could achieve those by bypassing Drupal in certain areas, routing requests through Laravel, and hitting the same database drupal was talking to (we had custom tables in drupal anyway, so updating them directly was never going to cause problems).
So the plan was to place, as you said, a Laravel/Lumen instance alongside the current app, talking to the same database, but taking advantage of the fact that Laravel's request bootstrapping time was something like 100ms rather than Drupal's 3 seconds.
Can that be done from other, non-laravel apps, without an actual HTTP request?
It can definitely be done from other non-laravel apps, but you will probably need a HTTP request, particularly if you're building an API, and one that you'll want to be able to re-use with a completely new app in the end.
You can definitely do this modular step by step replacement technique - just watch out for:
- Interaction between the old platform and the new platform's data - it could cause problems.
- Authentication is a major consideration - how can you ensure that the person calling the new API is who they say they are in the context of the old system.
- It's definitely going to increase the amount of maintenance you need, as you're adding in a new codebase.
- Measure any improvements the new parts of the system give you - speed, conversions etc.