I feel that lag is still manageable with MK. However, it DOES affect him more than other characters just because his moves rely on being instantaneous and he cannot be as agressive on his approach because the timing of all his attacks is off. Since most start and end so quickly, it is very easy to get punished out of timing errors. I also main ROB and I can tell you that he takes the lag MUCH more gracefully than MK. Spamming neutral-a is amazingly effective in the lag because of its amazing range, priority, and duration. If you fast fall it from above, I swear it almost never misses its mark. His projectiles are also easier to use in the lag. Overall, lag throws off more aspects of MK's game than most other characters (I'm looking at you Ike!) and while he is very capable, he will have to adjust much more greatly (which could throw off your timing for non-online play) or work a lot harder than others.
Trust me, just use MK when you have a very good connection or you are not playing online to WIN.