Well, I've never played any of those fighters you've mentioned, but I try to tell some tales out of school, based one some things I heard from other players and
Tenryuga told me.
Both Hayate and Jann Lee are well balanced characters with good tools for every situation, either close combat or range/spacing game. However, that means they are good at most things, but not best, and since you are playing Kasumi which is one of the fastest fighters in the whole game, you might take advantage of this.
Facing a solid Jann Lee player can be a pain and once he get you stunned you surely will have a hard time. I would recommend not to try out doing a spacing game against him, since most of his tools are better than Kasumi's for this. You can try it of course, the most important thing in this case is to watch when he is going for a his unblockable dragon kick. In general, it is easy to see when he is doing this move, but if you are playing online, it might be that you don't get the sidestep or crouching stance right before he reaches you because of input delay.
Staying at close range against Jann Lee might be the better option, but in this case, he can use his offensive hold (dragon gunner) to get into the stun game. Once he caught you with this move, it is a completely guessing game for what he's going after it. He can either go for a mid kick, mid punch, high punch or a dragon gunner reset. If you guess wrong, you mostly will eat a lot of damage.
So, I don't know any tool that works especial good against him, just use your fast jabs and 6P against him. You can try to stay a bit more away from him, in a range, where his dragon gunner does not catch you and retaliate with 3K, 66P or 66K if he whiffs this hold or other attacks. You might also use 1PP a bit more, if you do this and he is using his dragon gunner, you will beat him out.
When it comes to Hayate, you can also try to rely on your speed. Hayate is not very save on block, so don't be afraid to stand there blocking, trying to throw-punish after it. Against his special sidestep, use tracking moves like Kasumi's 6PK and 6P2K. Her P+K should also track and hit him while doing his sidestep. In general, Kasumi's most reliable tracking move is 6PK. Hayate is more dangerous at mid range, so better stay close to him. He also don't has much options after his guard breaks, he's running a 50/50 chance of mid punch or throw. If he lands a sweep, he should be respected, because a lot of his options will score a counter-hit, especially online. Hayate has almost no attacks or follow-ups that can be thrown out delayed, so if you don't see a follow-up come out immediately, you can try to attack.
Against Lisa, I would also recommend to try staying in her face. If she get's away from you, she is more dangerous because of her offensive holds, but in close range, she don't has a lot of options to get you off and you will beat her out in speed. If you have trouble with offensive holds in general, you can either try to use low attacks like 1PP or 2P more, or throw out a fast throw like 6T for example.
I'm afraid that this is everything I can tell you so far, maybe one of the other Kasumi/Hayate/Jann players around can give you some additional help.