...
The LFL will pick anything sector widethats in range, then once <playership> reaches <20km range the middle bar is filled, and at <5km range it will fill the top level. Once closer than 1500m, the discovery triggers and the object is considered discovered. Discovery points are then rewarded and added to the total and current pool.
The range of the LFL various depending on the object and sector, some things like the HSAP are sector wide, other things like ware crates/ships can have a limited range so the LFL might not trigger straight away upon entering the sector. However, generally you shouldn't need to go beyond the borders of the sector before the LFL will trigger if there is anything in the sector.