This is always the million dollar question, and anyone who answers that definitively without being in the water with your child, is either a rookie, or trying too hard to get your money.
Each child progresses differently, as stated above in the teaching tips article. We tell the parents to look for good progress. You know where your child began, and you see where they’re at. Withgood progress happening, keep supporting that progress. Commonly though, non-fearful four year olds and up in private lessons can pick up basic swimming in half a dozen lessons and be strong swimmers in a dozen or so lessons.
Your instructor can give you a truly informed perspective after the first few lessons. It could be a just 2-4 lessons for adults, a month or two of lessons for children, or into next Summer for toddlers. Support the progress, not a fixed date, and watch things come to pass with smiling faces in the water–not stress.