First off to explain myself, I am a math geek which is schooling for a math degree, I love math. Alright that said...

Has anyone ever attempted to see if you could do arithmetic instantly while lucid dreaming? Like imagine a calculator or some smart philosopher person and see if it worked?

Considering the amount of complex and dynamic realities your mind can create out of nothing, I am highly skeptical you CANNOT do simple arithmetic instantly, in fact I think you could probably do algebra or even calculus instantly.. "Hey philosopher dude, derive this function for me and find the integral a,b NOW"
"I said NOW, YOU'RE FIRED"