“That's a good question. Let me find out for you.”
Someone calls you at work to ask a question, but you don't know the answer. You need time to research the answer, so you say this.
That's a good question. Let me find out for you.
You say "That's a good question" when someone asks a question that's too difficult and you don't know the answer to. It sounds better in a business situation than just saying "I don't know."
When you're offering to do something to help someone, you say "Let me ___". For example, when your friend arrives at an airport and is carrying heavy bags, you can offer to help carry them by saying:
Let me help you with those.
When you use the phrase "Let me ___", it's common to end the sentence with "for you":
Let me look that up for you.
To "find out" a fact means to learn about it through reading or hearing about it from other people.
The object of "find out" comes between "find" and "out" if it's a short word:
How did you find that out?
The object comes after "out" if it's a longer phrase or clause:
She found out that Brad was involved with another woman.
And in some cases, "find out" can be used without an object, like in this example:
I'm not sure. Let me find out.
You can use it this way when it's understood what you are finding out. In this example, you are going to find out the answer to the question.