Lead a life / live a life

He can continue to lead a normal life

Here, lead means to have or experience.

It is not a general synonym for live.

When can it be used? Can you "lead happily forever after"?

When lead is used to mean to have or experience, it can only be used in reference to a life. It is not used in any other context. So you can’t say lead happily forever after.

However, you could say: he led a happy life.

Figuratively, life is a path. A path may lead us to a place; we do not lead the path - we follow it. Similarly we may follow a life of simplicity, for example. Perhaps this seemed too passive for an obituary of a great leader and so was changed to "lead" and the phrase stuck. I'm only guessing.

My take on it is that "He/she lead a good life" would mean that the person conducted himself (herself) in an honorable way during his/her lifetime.

Whereas, to say "He/she lived a good life" would mean that the person enjoyed their life in which they were happy (happy, healthy, successful, etc.).

So "lead a good life" implies some moral judgement, whereas "live/lived a good life" implies only personal happiness/success.