This depends on the parents, student and the tutor. In most cases, it is preferable if the tutor and the student have the lesson without someone else present in the room. This allows both the tutor and student to be completely free so that the child can take the full benefit of having private lessons with someone that they do not necessarily meet every day. This applies to both face-to-face lessons and online lessons.
Sometimes, especially in the beginning, it can be reassuring for both the parents and the tutor if one of the parents are present during the lesson. It might also be helpful for the parents to occasionally be present to see how the lessons are done. This ultimately comes down to what you decide with your tutor, so it might be worth asking them about it.