Pursuit and Line (Draft) movement work exactly the same as Thunder Alley. You can move laterally, but once you move forward the car links and cannot change lanes the rest of the move.
I don't think this is stated exactly correctly. I believe a car may move forward and changed lanes as long as it is not linked to other cars. The rule states that Pursuit and Line movement are exactly like solo movement until they move forward and are linked. So, for example, a car could move sideways out of line, move forward x number of spaces, duck back into the line (possibly by displacing a car), and move forward finally establishing a link. At that point, it may no longer change lanes.