Would one voice lesson a month noticeably help or not? Once a week is good right?
It could. More important is the time you spend applying what you are doing in the lesson, practice. If a student doesn’t practice regularly, a little every day, trying what the teacher has suggested, then certainly 1 lesson a month is not going to be very helpful, and maybe a waste of time. Singing is a "do it yourself" thing, only you can develop your voice using the advice of a good teacher. It’s not like math where we could borrow someones home work. A 30 to 60 minute lesson every week would be best, depending on the person’s maturity and experience. Regular practice is important , and patience, over a long period of time.It takes a while to develop and improve the delicate singing mechanism.