On the Underground: London/Berlin

Does the Passenger always choose to use a line when moving to its Destination?

It depends
The Passenger selects which route to take by following the a set of 2 rules in this sequence - The Passenger will choose the route that involves the least amount of empty track spaces & then the route that with the fewest (or even no) lines. Sometimes, it might happen that the Passenger to take a route that won't use any of the lines.