Doomsday is one of those matches where it's over after the first hit imo. The minute either character gets started on the other, you're either eating loads of damage (Lobo) or you're getting sent into the corner (DD).
Honestly, the way I play this matchup is by trying my damndest to keep him out and try to punish him to get a life lead/trait load. I use b12 a lot in this match-up to keep him still in that close-mid range. Once DD activates trait, I just try avoiding him at all costs. We don't have anything that runs his trait out like Green Lantern's minigun or Raven's F2222 on hit, so our options are: try blocking everything he does or run. One of the most important things about the Doomsday matchup for any character is establishing the mind game from D1 xx ES; that being, backdash before the ES. After the DD player sees that, he has to start making guesses like D1, dash forward/d1, sweep/d1 xx shoulder, and all of these options are unsafe/minus enough to allow reversal pressure. Once he has to guess on his offense, it's a bit easier to deal with him.
Random notes about the match-up: Learning how to stuff all his wakeups (except up shoulder) is key, obviously. DD's corner reversal is null on Lobo, Hook Charge MB reacts weird in the scenario and allows him to get out of the corner/knockdown DD. It's hard to explain,, but try it out for yourself. It's kinda funny.