My friend wrote something, and there's a line in that something that reads:
If you would look it up, you'll find it is a noun.
She was talking about what some word means. Anyway, that's irrelevant here.
Is that line grammatically correct?
Shouldn't it be
If you would look it up, you'd find that it's a noun.
or
If you looked it up, you'd find that it's a noun.
If you would look it up, you'll find it is a noun.
The sentence does not sound natural to me. The use of "would" here is unnecessary, but it seems particularly common for German speakers learning English.
Your first alternative sentence uses "would" in the same way, and so it also sounds unnatural to me:
If you would look it up, you'd find that it's a noun.
Your second alternative, however, sounds just right:
If you looked it up, you'd find that it's a noun.
The "would" (abbreviated into you'd) is now in the dependent clause of the conditional. The word "that" (like the word "then") is optional and does not affect the meaning.
All the sentences below are grammatically-consistent ways of expressing the same idea:
If you looked it up, you would find it is a noun.
If you were to look it up, you would find it is a noun.
If you look it up, you will find it is a noun.
Note that the last one contains contains no "would" at all.
