Depends on the HP. If you threw 999 Poke Balls a paralyzed Lugia (paralysis because that's the only way that it wouldn't have Struggled to death by that point) with 1 HP, your odds of catching it would be 99.999989951% - so pretty much, yeah. But if it were at full HP, your odds of catching it would be only 98.176%. Still incredibly high, but a roughly 1-in-55 chance of not catching it is still lower than the Master Ball.

...Of course, if you factor in how incredibly unlikely it is that, in 999 turns, it would have been fully paralyzed so many times that it still hadn't Struggled to death, those numbers would change, since the odds of you getting to throw 999 Poke Balls at all are very low.

Assuming it's at level 50 in Alpha Sapphire, Lugia would need only 24 turns to Struggle itself to death: 5 each to deplete the PP of Punishment, Aeroblast, Hydro Pump, and Rain Dance, and then 4 each for Struggle, if it's at full HP. Assuming you paralyzed Lugia before it launched a single attack, you would need Lugia to launch an attack less than 24 times within its first 999 turns in order to launch a Poke Ball (Turn 1 included because you can't throw a ball on the same turn that you paralyze it; Turn 999 excluded because you'd throw the ball before Lugia is able to attack.) If it is fully paralyzed at any fewer than 975 times, then it will Struggle itself to death before you launch Poke Ball #999. The odds of it being unable to attack 975 times in 999 turns come out to, I think, 0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003131513%.

So.. chances are, you aren't going to get to throw 999 Poke Balls at a Lugia, or any other Pokemon for that matter. :(

(You could go with sleep instead of paralysis, and that would probably make your odds MUCH higher, but that'd also be way, way harder to calculate.)