Praise be to Allah.
In order for wudoo’ to be valid, it is essential to remove anything that will prevent the water from reaching the skin, whether it is lipstick or anything else. But if the colour or trace of it is left, even if the water touches the skin and runs off it without sticking, then wudoo’ is valid.
Al-Nawawi said in al-Majmoo’ (1/492):
If there is wax, dough, henna and the like on one of his limbs, which prevents water from reaching any part of it, then his tahaarah is not valid, whether the amount is large or small. If there are traces of henna and its colour left on the hand, without there being any solid material left, or elsewhere, or traces of liquid grease whereby water flows over the limb but does not stay there, his tahaarah is valid. End quote.
Based on this, you should remove the lipstick before you do wudoo’, so that there will be nothing left that could prevent the water from reaching the skin, but if the colour or a trace of grease is left, that does not matter.
And Allaah knows best.