First of all, Rosie, I'm assuming you are talking about your kitchen units?
With "proper" liming wax, it is wax, so overpainting is usually a big NO. The wax acts as a release agent, and throws off any subsequent paint coats.
You get around this by trial & error. Lots of hard scrubbing with wirewool or a stiff scrubbing brush dipped in plenty of white spirit. Even then, ingrained wax can still be a problem. You just have to give it a go.
With modern kitchen units... I don't know, but I would be surprised if mass-produced units are actually finished with wax. More likely to be simple white paint diluted, left to get into the grain, then rubbed back to give the liming effect. Possibly then sealed with acrylic or polyurethane.
I've done this myself plenty of times.
Overpainting that would just mean a good rub down and , preferably, an oil-based undercoat and finish coats.
This would obliterate the original completely, which I guess you don't want to do?
I can't quite understand what you mean by lightening the finish.