This mission is not really that much different from the ones before it. All you're doing is capturing a single Drengin planet, which is not very well-defended and not too heavily populated. But you have to do it while the Dread Lords rain down on you like the wrath of the gods. What I did was, colony rush (the initial three, plus the next two left, plus the next one left-up, plus the center, plus the next one left-down), constructor rush (a throwaway military starbase by the DL world to see what they're up to, economic starbases by my two manufacturing worlds, and eventually a military starbase just in range of the objective planet). You star with enough money to buy all this every turn, and if you don't finish the mission flat broke or even deeply in debt you're probably doing something wrong or cheating.
Lowering the difficulty in campaign maps where it's you and allies vs the Dread Lords (or trying to avoid the Dread Lords in this case) just reduces the survivability of your allies to zero. Since lowering the difficulty doesn't really make the Dread Lords any easier, you might consider doing the counterintuitive thing and raising the difficulty so at least your allies are smart enough to provide an effective screen. That would be 'Tough' difficulty or above. Above that all AI also gets bonus multipliers. I lost once on Normal, thought about it, read some very innovative strategies in these forums, thought about it some more, played again without changing the difficulty, and won in a rather dramatic fashion, with literally one troop transport to spare, and with the DL battleship literally one turn behind it, having lost three planets to the invasion forces.
It may seem like raising the difficulty would not be a good idea, because it's 3v3, but your 3 are allied, and their 3 are actually 2 and 1.
Bear in mind fully that the objective is to take the Drengin planet. Not to build a flourishing empire at your starting point. You need to get to the left side of the map muy rapido, and you might need to trade tech with your allies.
If you can take and hold the center star, Primus, for long enough to turn that planet into a massive research outpost, you can tech up to planetary invasion and even planetary bombardment before the hammer fully lands on you from above. You will probably lose Primus first, though. Then one of your core worlds. You will have to ignore this. By then you had better have fleets already heading towards the invasion, because right around that time your economy might go very negative. At least mine did. Also, you don't personally need to capture the objective planet. Your allies can also do it if they get around to it.
It's also much easier to take planets from the Dread Lords than it is to hold planets from them, provided they are undefended. Those 10 guys are tough, but when you attack they die easier. But this shouldn't come up in this mission because as soon as you gain the ability to invade planets there's only one you should be invading, and you should be invading it with everything you have in a Hail Mary play.
Alternatively, you can also just lose this mission fair and square and do the alternate one. By comparison, it is dirt simple.