Can a person ask in prayer for certain events, or even entire lifetimes, be hidden from inspection by physical intuitives in our akashic records? Would that be enforced? What is most important for us to know?

This cannot be done and is one of the ways in which the Law of Karma holds power over you, because there are no secrets, ultimately, so even if you attempt to obscure things it will only work to block those with modest intuitive ability. But we can tell you, in the heavenly realm everything is out in the open on display. This is one of the reasons why light beings are trustworthy and find harming others to be unthinkable, because they do not want it on their record. That system would lose its enforcement power if a wrongdoer could simply cover up their misdeeds to make them invisible.