"continuations" are not in standard Common Lisp. They are a Scheme feature (-> functions which capture a state of computation). Common Lisp has a standardized exception handling system called the "Condition system", it features conditions (-> exception classes), handlers and restarts. It provides a non-terminating exception handling system, also often with a user interface -> the user can choose a restarts via some menu system or in the REPL. Something similar is in Smalltalk, which provides excellent tools for error handling and debugging.

Lisps prior to Common Lisp usually had elaborate ways to handle runtime errors and extensive REPL interfaces for it, for example the break loop -> a REPL in the error context. The most prominent and widely cited was the one of Interlisp, which featured also user facing automatic error repair (-> DWIM).

Whenever I see a Lisp, which doesn't stop at an error and then let me look at it, I feel sad.

GNU Emacs is an application (a text editor) -> debug-on-error is by default NIL. That makes sense in an application.

> that never became a thing everyone wants, I guess it's not as critical as you paint it to be.

People asked for it, it seems. But the answer was no.

See for example "https://vimeo.com/223309989", "REPL driven development". It was a topic in the Q&A at the end.

Also: Since JVM/Java already has a built-in exception handling, why build another one?

There are some libraries...