Are "Let's say..." and "for example" used in almost same situation? Are they used interchangeably?

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They don't mean exactly the same thing, but they are usually interchangeable without one being wrong.

"Let's say" proposes a hypothetical situation to explain or work out a concept. If I'm trying to walk myself through creating a mathematical formula or writing a computer program, I might say "Let's say that the number 5 is input, then I'd need [some other number] as output, so I need to [some action].

"For example" uses gives an input and output to explain a concept. This, and not "let's say" is usually used in questions on worksheets and tests in school.
-"For example, if Mary has 5 objects, she can line them up in 120 different ways."
This just makes sure that the reader understood what the question was saying.

Perhaps a more important and noticeable difference is that I feel that "let's say" is more common is speech, and "for example" is more common in text.