This is a profoundly short-sighted and ignorant position for many reasons.
1. You will give far more publicity to LulzSec than they are already getting by acknowledging them as such a severe concern you've pulled your engineers off other more valuable tasks to enact draconian and totally meaningless interdiction efforts
2. It won't actually shut them up. LulzSec is an example the ultimate asymmetrical enemy. They have fewer numbers, fewer financial resources and less technology, but have a mastery of the terrain. You don't defeat a guerrilla by pretending they don't exist. You do not attack them where they are strongest.
3. You're not actually achieveing anything here. Twitter isn't exposing itself to legal vulnerability here, and you certainly wouldn't shut up LulzSec for even a split second by just taking away their Twitter account.
I mean, honestly, have you thought this through at all? Have you paid attention to anything in the last 20 years? This kind of short-sighted feel-good finger-in-the-dyke measure is exactly why we're all sitting here screaming into the wind about copyright and piracy. What a shame that there are so many people who think this is the way to handle serious issues on the Internet.