Welcome to TCS. I'm sorry for what's up with your two kitties, but there are things you can do to help.
Straight off, I'd say add two more litter boxes. The rule of thumb is to have one more litter box than cats, but with this situation, I'd add two, both uncovered, and in very different places.
I'd consider purchasing Feliway spray and using it around the apartment or house regularly (nowhere near the litter boxes or where they're supposed to scratch). It is a synthetic hormone that mimics the "friendly" markers in cats' cheeks, and it helps promote a "calmer" atmosphere.
I would also consider purchasing a Bach's Flower Essence of some kind to add to their water - either Rescue Remedy or Calm and Serene. You can also dab it behind their ears and at the base of their tails. It doesn't work for all cats - but when it does work, it helps, so it's worth a try.
Forget the water bottle. All it does it get the cat angry with you.
Cats are very much like toddlers, and they need positive reinforcement as much as they need to understand behavior that is not OK.
There are some things you can do to help them come to associate each other with "good" things. This should have been done during a long introduction period while they were separated when you first brought home Lexi - but most of us didn't know any better when we brought our second kitties home either, so to just work from where things are at this point is probably best.
I'd take a several clean rags (preferably washed and dried with no fabric softener). Rub Lexi all over with two of them. Rub Zelda all over with one.
With one of the "Lexi" scented clothes, put it under their food dish (if they free feed). If they don't free feed, when you feed them, put the Lexi-scented cloth under Zelda's dish, and put the Zelda-scented cloth under Lexi's dish.
Give each of them at least 10 - 15 minutes of "alone time" play every day (take one into a room where you can close a door with a favorite wand toy). Play helps relieve stress. When the play session is done, put down treats on the rag that smells like the other kitty.
Whenever you see them near each other without Zelda being aggressive, praise her to high heaven, and give the two of them a couple of treats (because of the amount of treats you'll go through over the next couple of months, limit each "treat" giving session to just one or two each time).
Make sure to give Zelda attention first: pet her first, put her food down first, etc. The reassurance that she is still your "number one" kitty may help reduce her stress about that horrible cat invading her space.
When Zelda is cornering Lexi in the litter box, walk over there and blow a short, sharp puff of air directly in her face. You may have to give it two - four puffs really quickly (all our kitties except Flowerbelle react to just one - Flowerbelle takes 3 - 4), say "no" and if you can, pick her up and give her a "time out" in some room for a few minutes.
The idea with ALL of this is to
1) Help Zelda understand she's still "top cat" in your book;
2) Help Zelda think it's a total party having Lexi around;
3) Help Zelda associate Lexi with things she loves;
4) Help Zelda understand what behavior you do not think is OK.
BTW - are they both spayed? If not, they need to be, ASAP. This will help reduce aggression.
Also, do you have much vertical space for them? If not, consider adding some cat trees or cat walks on the walls for them. Being able to go "up" can really help with the cat dominance problem. We bought open-sided book shelves for the kitties and attached "ramps" to the sides. Others have "built" rubbermaid "pyramid" towers and such, cutting out access holes, but building lots of levels.... there's lots of ways to do it.
Just like with young children, changes won't happen overnight. But keep at it, and you'll see improvement!
We live in a situation where it is not possible to separate cats for introduction of newbies. We HAD to adopt our seventh - Billy - this last November. He'd been living outside for all of his two years. Our alpha, Lazlo, decided he did NOT like him. So Bill's been here 5 months now. Lazlo still growls at him and lunges at him - attacking him - but it is FAR less frequent. We've gotten to the point where in the bedroom Lazlo is OK with Billy being around. Billy can even put his face right in Lazlo's, and all Laz will do is sniff!
In the living room... it's a toss up for poor Billy. He just doesn't know whether he'll get chased/attacked or not. Usually not - but.... However, this is a total improvement from being attacked ALL the time, everywhere, and being chased out of the litter box.
So be consistent, and just keep at it!
BTW - others have recommended the "vanilla" trick. This is taking a little vanilla and dabbing it on each kitty every morning and evening. The idea is that it helps "confuse" the smells - and Zelda is reacting to having a kitty invading her territory. This did not help our situation. It is something you can feel free to try, but we've had much better success with getting Lazlo to associate Billy with "good" things (Lazlo is very food motivated).
If Zelda is food-motivated, I'd go for the rewarding non-aggressive behavior. No matter where Lazlo is, he'll eat treats head-to-head with Billy. So Lazlo knows that when he's not mean to Bill he gets rewarded, and when he attacks Bill, he gets a time-out in the bathroom for 10 minutes. We've even gotten to the point where they'll both play with the same wand toy at the same time - Billy up on the cat tree, Lazlo on the couch. Toss it to Bill to grab, toss it to Lazlo to grab... At first, Lazlo would ignore the toy and go directly for Billy.
Now they know that when they "play nice" they both get treats (right next to each other on the living room floor) when they're done. Little by little.