I was supposed to order a book on online for my friend, Since I was busy in my work, I didn’t have the time to check my friend reminded me to check, So I replied I will look up to that But she pointed out my mistake and replied I will look up that But, I think what I texted was correct. I will look up that doesn’t seem to fit in. Or does it?
Neither of your answers is correct.
"I will look it up" is correct and natural English.
"Look [something] up" is a separable phrasal verb. With most separable phrasal verbs, it's optional whether the object separates the verb or not:
I will look those things up for you.
I will look up those things for you.
Both these sentences are correct and natural, and have the same meaning.
BUT, if the object is a pronoun, then the verb must separate. The object in this sentence, "that", is a pronoun, so "look up" must separate:
I will look that up for you.
I will look up that for you.
To "look up to something" has an entirely different meaning:
to respect and admire (someone)
// I've always looked up to my older brother.
// The kids really look up to their coach.
"I will look up to that" refers to you physically looking upwards, which would often be correct, however, because "looking [something] up" is more of a figure of speech rather than something meant to be taken literally, it plays by different rules.
If one is doing some research on a particular topic or just searching for something - especially on the internet - they are said to be "looking up" said thing or topic. "Looking up" is almost treated as a single word here in some ways.
In your case, there are a couple of correct ways to phrase it:
- I will look that up. (More common)
- I will look up that.
You don't say it as if you are going to physically look upwards in order to see the thing, you're just looking it up. We have some funny figures of speech!