They're refusing to hand over data to the FBI about visitors to a Trump-protest site, so if this is more than a co-incidence, then we're possibly looking at internet-savvy "Pro-Trump" folks. Since we know 4chan was a huge congregation point, I'd wager they're just a bunch of folks using LOIC to attack DH, or some DNS amplification attack.

Edit: Interestingly enough, this is going on even though the DOJ amended their request to be more focused (they claimed to not understand exactly what they were requesting, which is just as scary). So, DH will probably comply now, but the attack rages on. http://fortune.com/2017/08/23/doj-dreamhost-anti-trump/