I am currently living in an apartment with another female. My name is not on the lease - just her name, her daughter's name and her sister's name. We signed a roommate agreement but I am not happy with the living situation. We agreed to a 60 day notice after lease has terminated - at least that is what the copy of the document she gave me says and it looks as if the document was altered before she gave me a copy. Can I give her a 30 day notice and be done with it?

If you signed a personal agreement with her, you are legally bound to it, unless she is breaking some law.
About it being altered - didn't you get a copy right away of what you signed?
I also don't get the part about agreeing to 60 days after the lease is terminated, since that doesn't sound possible, unless she knows that once her current lease is up she is a tenant at will. But what does it say about notice before the lease is up?
The best course with any roommates is direct communication rather than legalese, at least at first.
She might be happy to give you 30 days if you aren't getting along anyway.
Answer below to explain a little more (also what state this is in)?

I could not find my copy so I asked her for another copy.

I also don't get the part about agreeing to 60 days after the lease is terminated, since that doesn't sound possible, unless she knows that once her current lease is up she is a tenant at will. But what does it say about notice before the lease is up? - This is my confusion as well - it reads (typed) If any tenants wish to be released from the lease they must give 60 days (I'm fine with this) notice to the other parties and in handwritting it states after lease has terminated.

State of VA

Since you lost your copy you are stuck with what she gave you.
The written part added on makes no sense to me, unless as I suggested maybe she has a one year lease and knows she will be a tenant at will after that.
Give her written notice today for 60 days, that's all you can do.
Ask her if she is willing to change it to 30 today.
If she's experienced at this she knows that people can skip out, leave town, leave the state, and she's better off compromising, given that you all have to share the same space.

I think the handwritten part is unenforceable since it makes no sense. Notice needs be given BEFORE the lease is terminated. So give her notice and ask if she will allow you to vacate before the 609 days is up.