A guy plans to invite a girl to a date but she is busy at work. He texted her, asking when she will be back. She replied that she will be back around 11pm. He thought
23...結構遅いな、そりゃ起きてはいるだろうけど彼女の疲労度合いが不安材料
He debates whether it is worth asking out tonight.
I am not sure what he means by「そりゃ起きてはいるだろう」. Is it referring to the fact that she is awake at 11pm? It is not clear to me what そりゃ might refer to and whether 起きる means being awake.
As far as understandable from the provided text, the speaker is worrying if 11pm is too late to ask for a date.
起きている should be awake.
The use of そりゃ is subtle. It is a contraction of それは. Practically I think it is better to think it as a pattern: そりゃAだろうけどB, meaning Of course, A is true, but one must take into account/think about B. B works as a reservation with respect to A.
Example:
The phrase means: 11pm is late. (as for being awake or not), of course she'd be awake, but she may be too tired.
First of all, to answer your questions about そりゃ and 起きる.
そりゃ is a auditory contraction of それは and the それ points roughly to "the situation as it will be at 11pm." It is panacea word somewhat like "stuff" or "thing" in English in the sense that it fills in for something more specific without having to come up with the precise words.
起きる means wake up, but actually the sentence you have is using 起きている, meaning awake, only the particle は is stuffed into the middle. The は is being used here as a marker to indicate contrast. On the one hand: awake. On the other hand: tired.
Now on to the sentence as a whole; as you probably know, Japanese omits subjects and objects very often, so that you are forced to infer what they are from context. If you can provide more context than that single sentence, this answer would become less guesswork and more authoritative.
Having said that, I would posit that in this case the subject of 起きてはいる is the guy, not the girl, as from the fact that she's only just getting home from work just then that she would be obviously be awake at that moment (unless she's a sleepwalker?). The positioning of 彼女 in the sentence reinforces this interpretation in my mind.
23時・・・結構遅いな、そりゃ彼女起きてはいるだろうけど疲労度合いが不安材料
to me would be more natural if both "awake" and "exhausted" both referred to her.
He is thinking to himself, "11pm... man that's late. Yeah, it's true I'll still be up then, but she will have got to be dead tired after working that late; that's the real problem here."
