WRD Air valve

[alpina]

I am in the process of cleaning the Warm Running Device. The Air valve was well a truly stuck in the air valve housing. After much work WD40
light taps.. harder taps... much harder taps I managed to get the valve moving and finally apart. so the question is what it the best thing to use to
lubricate the valve went I put it all back together ? engine oil, grease ?

thanks DM