The delayed triggered ability created by Brass Infiniscope's ability resolves before the spell that caused it to trigger. It resolves even if that spell is countered or otherwise leaves the stack without resolving. In that case, use the value of X as that spell last existed on the stack to determine the value of X for the delayed triggered ability.

You'll only gain half X life no matter how many instances of are in the mana cost of the spell you cast.

The value of X in the delayed triggered ability created by Brass Infiniscope's ability is the value of X of the spell you cast as it exists on the stack when that ability resolves. (Usually this will be the same as the value chosen for X when the spell was cast.)