He can still parry you while you're in trait. If you time your d1 properly on his wake up, you'll hit him out of his animation, and he won't be able to jump out of the corner. Raw ES will also send him back to the ground but you'll get a weird knockdown that you can't really oki off of.
It's a weird match up but if you play it properly it's most likely 6-4 in DDs favor. If you stay on him when he doesn't have trait there is absolutely nothing Lex can do. You have to be patient and not get hit by random shit while staying on his ass and forcing him to block.
Source: I play rev0lver all the time and I don't actually downplay this character, people just think I do because I'm realistic.
Also Doomsday loses 6-4 to both Batman and Aquaman. I was almost leaning toward Superman being even recently, but divepunches keep that match up a 6-4. I know @
Yoaksssss was the one saying they were 5-5 but I don't know where else to put this so yeah.