Yes, you can theoretically use lemon or other citrus juice, but the practical problem is most people don't know the citric acid content of the juice. Not knowing the citric acid content of the juice means you can't accurately calculate how much extra NaOH to add to properly neutralize the citric acid.
You can guess (and I talk about that in my article about citric acid and citrus juice
in the "acids" section on my website), but in the end it's a guess. The more citrus juice you use, the larger the potential error from guessing. That's why it's wisest to stick with citric acid powder because it's a known quantity.
You
have to add extra NaOH to neutralize the citric acid. If you don't, the superfat will be overly high and you could end up with the problem in lsg's video. But you also don't want to add too much NaOH because you could end up with a lye-heavy soap.