Frome the Avalon Hill FAQ:
How do Lightning Assaults work?
This advantage does one thing: It lets you get around the normal restriction that a transport has to stop when it unloads. So, here’s precisely what you can do with a lightning transport: Load up 2 infantry, say, in Sea Zone A. Move one space to Sea Zone B, and drop off one of those infantry on an enemy territory. Then, move your transport again to Sea Zone C, and drop off the other infantry in a different enemy territory. You don’t get to move the transported land units twice, or have the transport carry double capacity, or anything like that – Lightning Assaults only gives you the ability to “split” your landings between two neighboring sea zones.
Here’s the situation: Japan sends a transport carrying two infantry, along with a battleship, to capture two territories using Lightning Assaults. The transport splits the infantry between the two territories. Can the battleship fire on both of them?
No. Lightning assaults affects only transports, it doesn’t give a second shot to the battleships.
Does Lightning Assaults increase the transport’s movement from 2 to 4?
No.
Complete FAQ is available here:
http://www.wizards.com/default.asp?x=ah/faqs/axisrevised
@hondo:
do you use the same ground units in the 2nd amphibous assult? for example, if i have 2 infantry on a transport and i invade somplace with those 2 infantry, i then pick those 2 infantry back up on the same transport and go someplace else(with in the transports aloowed movement)?
The situation you are describing is not a legal move.