While this mission is easy for this part of the game, getting the plans on the southernmost Neutral City on the island might be a bit trickier. Start capturing the Docks, then build a Battleship as soon as you can and when you have the funds (should be in 2 days) make a lander with an infantry or mech and an anti-air. If you go for it too fast Lash will send a Bomber there and make the capturing a nightmare. This speed should help make Lash only send one Battlecopter. If you fail you can even try again with a second Lander and a cruiser escort.
The main mission is pretty straightforward: Proceed with your main force taking care of your Md. Tanks, keep your Rockets and the other Anti-Air safe, and just push forward checking the range of the cannons. The initial push shouldn't be too hard, use your APC/Tanks as bait and then counterattack.
Lash will try to keep her Rocket just out of range but you can get to it with your power and easily destroy it. The southern cities will be defended by an artillery you can most easily take out with your Recon, that way the main force can continue advancing.
To deal with the cannons you can use your Md Tanks or blast them from safe distance with your Rockets. A combination of both will take one out in a single turn. Sending one Md. Tank left and one right will be the faster option, but watch out for the cannons range and the air units.
The ships will take the most damage from indirect fire such as Battleships, Rockets and Artillery, however don't forget to make a couple Anti-Air to defend from Lash's Bombers and Copters. You should only need to build these units to complete the main mission unless something goes wrong. Split your fire to make the ships combine and take them out with less targets.