Choosing the correct lubricant for stabilizer wires is a bit different to choosing a general lube for other parts of a mechanical keyboard. For stems, springs and casings, we want to reduce friction and prevent uneven wear. For stabilizers, the job of the lubricant is not only to provide a smooth action, but also to prevent the ends of the wires from rattling as a key is pressed.
To this end, we need to choose a lubricant which is far thicker and more viscous than we might choose for other parts of a keyboard.
We have a number of products available which will work well for this purpose, the crowning jewel being Krytox XHT-BDZ, which is deliciously thick and creamy while still being soft and easy to apply.