'flutter_map' is in no way associated or related with Lima Labs.
Lima Labs' home page: maps.lima-labs.com Lima Labs' pricing page: maps.lima-labs.com/index.php/pricing
If you're looking for extremely low cost & often free (even for commercial usage), but still reliable, and low frills service, Lima Labs provides high quality raster tiles with one style based off the standard CARTO style.
Sign up for an account - Lima Labs operates manual verification, so you may have to wait a few days
Use the common URL (https://cdn.lima-labs.com/0/0/0.png?api=___) with your API key