- Yes そりゃ means "that's" in this context. それは/そりゃあ is often used at the beginning of a sentence, like an interjection, to indicate the speaker is trying to give some explanation (≒ "Well, that is to say, ...", "Er... that's...")
- まあ is like "you know" or "well", and used before saying something unexpected, unimportant or something the listener may already understand. It makes the statement softer.
- ねえ is like "... huh?", "... isn't it?" or "you know?" used to show a positive response is expected.
Put together, そりゃまあねえ can imply something like "Oh, that was .... expected", "Um, yeah, why not?", "Well...that's because...don't you know?", depending on the context. Basically, the speaker cannot (or doesn't want to) say something clearly, but wants the listener to understand what he/she is going to say at the same time.
A: あの人のことが嫌いなの？ どうして？
B doesn't want to state the reason explicitly, but is expecting A would guess it.