Zyprexa can cause drowsiness when you first start taking it as can Lithium. It takes time for the body to adjust but if after a couple of weeks she is still very sleepy it would be worth discussing the Zyprexa again.
Lithium is different for everyone but can cause drowsiness when you first start it, although that doesn't mean it definitely will. I found I was drowsy for the first couple of weeks. Most docs advise taking it at night for 2 reasons, one because of the drowsiness (if you get it) and also because of something to do with absorption, which I won't go into because I'm not entirely 100% sure about the facts regarding that.
The Zyprexa is obviously acting quickly in calming her to the point of sleepiness but the Lithium won't have such a dramatic and quick effect. As ILAD has said it is worth reading as much as you can about both meds so that you are fully aware of all possible side effects, what to look out for and when there is something that needs intervention.
It's also really important to note, these drugs don't work overnight, other then heavy anti-psychotics.. Lithium is a fantastic drug and it works fairly fast. I went rapidly downhill when I was finally weaned off the Cymbalta that I was on. Don't change the meds at all until you speak with her psychiatrist. Some drugs, especially the anti-psychotics can make a person quite drowsy at first, but it's better then her outbursts right?? The Lith is safe, very very safe. and doesn't usually cause drowsiness, give the meds a little time to work. Hang in there.
I would not change her medications without speaking to her psychiatrist. If they thought she had bipolar and took her off Prozac that would make sense because that can worsen mania. Zyprexa is an antipsychotic that is a good mood stabilizer but that is sedating. Abilify is less so but as you said she couldn't tolerate it. Lithium is worth trying. Its the most effective mood stabilizer out there. For myself I found Lamictal had less side effects and was more tolerable but every person reacts differently. The first priority is for her to be stable so its best to let her take what she is prescribed. Then as she stabilizes you can speak to the psychiatrist about other options. A good website for all mood disorders is "Depression Central". You can and should inform yourself and speak to the psychiatrist. Just don't over ride their judgement.