Does lemon juice help breakouts?

Be careful. The peel oil is used as a wood cleaner and polish, where the solvent property of d-limonene is employed to dissolve old wax, fingerprints, and grime. A halved lemon dipped in salt or baking powder can be used to brighten copper cookware. The acid dissolves the tarnish and the abrasives assist the cleaning. As a sanitary kitchen deodorizer the juice can deodorize, remove grease, bleach stains.
Tough to say. There are a lot of anecdotal reports of things like lemon juice, clay, and some cosmetics improving acne. What does anecdotal mean? It means that someone tried it, and says that it works. The problem is that anecdotal reports are not evidence. Sometimes a home remedy seems to work, many times they don't. At this point, there is no real evidence that lemon juice improves acne.