Originally Posted by Niccias
Just farm with your Q, get RoA to keep your mana up, make sure you get blue buff. Your karthus, dont worry about killing her, since its very difficult w her spellshield. Just hit R and get kills across the map. Make sure you dodge the Q or youll die. Just sit back, farm up, wait for jungle ganks and hit R
I don't play karthus but I do play morg and this seems like pretty good advice. Morg isn't really able to kill somebody herself unless she can land Q or flashes in to ult. Her Q is only of the slowest skillshots in the game and it's blocked by minions so you really shouldn't be getting hit by it unless you're being lazy. If she flashes in to ult you then you flash out, that's the reason you took flash isn't it? Also remember to ward so you don't get ganked by the jungler, Morg is able to support jungle ganks really well and karth doesn't have a natural escape.
Otherwise you just want to try to stay even with her farming. Morg farms really well but Karth farms pretty well himself and will outscale her late game. So if you stay even you're technically winning when you think about it. You're not really going to be able to get kills on morg early unless she's dumb, she's a really safe laner, that's one of her biggest strengths.