I played over 2000 games with batman so listen up.
Batman's 223 string can be interrupted with a d1 after 22. I don't know how good Lobo's d1 is so you're gonna have to test it in the labs.
113 can interrupted after d1 after 11. Just like the 223 string.
If you want to know how to block his j2, you're just gonna have to practice with another Batman player to figure out the range. It's actually easy to block once you know the hitbox. Plus, if you can block Batman's j2, you can block any other crossover in the game. His j2 is nothing magical once you know how to deal with it.
If he tries to cross you over with trait, jump back and hit him with your biggest hitbox air attack (sorry I don't know any of Lobo's moves). Even if he hits you with his j2 when you're attempting to do this, he won't be able to get a big combo off or will just be forced to b23 and settle for about 20ish% damage.
On wakeup, you shouldn't worry about parry. Nobody ever uses Batman's parry more than once every 30 games. If he likes to slide, bait it. Pretend you don't see it coming and then quickly crouch block. The rest of his wakeups are extremely punishible and obsolete.
You just have to be patient when playing against Batman respect his pressure. His wakeup game is the vulnerable. So you should take advantage of that.
If he has you at full screen, carefully dash in and watch out for grappling hook. You're gonna be forced to play very good defense in this matchup