I'm a Schemer, and Scheme IS a lisp: we don't have restarts, but we do have call/cc, and images as Lisp has them are an optimization hack in any case. And we're finally getting some well supported implementations. Yes, we have hot code loading in most implementations.
Come to the dark side, we have (lexical) cookies (encoded with the current continuation after baking, of course).
Image dumps are also a useful way to create applications or use pre-assembled program state during development. Makes faster startup times, than loading objects during start each time.
Even an editor like GNU Emacs boots up a Lisp image. Which makes it much faster than loading code at start.
I would be very irritated if my Lisp Machine on start would reopen all network connections... But it has a controlled restart process, where I tell Lisp what to restart on a reboot. Actually a Lisp Machine has a list in memory, where the restart tasks are kept. If the image is restarted, one of the tasks it does is to go through this list and execute the various restart tasks...
Anyways, Lisp images don't work like that: a lisp image is a static preloaded environment. If you redefine some functions, exit lisp, and reopen the interpreter, those redefinitions won't be there.
If I save and load an image, the new definitions are still there.
What you refer to has very little to do with imags, Smalltalk keeps a database of code in files under system control. That's also how Interlisp worked.
On a Symbolics Lisp Machine I would configure the machine, load my software and create an image. After starting that image I would on login load any changes from the code bases. If this would be too long, I would save an incremental image.
The Lisp Machine had many more image related features...
In any case, at least a few Schemes have images, so it's a moot point in that debate. It's still interesting, though.
Oh, something like LispWorks has extensive support for using images, too. It has a very extensive application/library delivery mechanism based on images.
LispWorks can also save 'sessions', even automatically as periodically timed events. Even without quitting Lisp. Sessions are basically IDE states (files, listener history, lisp image, windows, ...).
Clojure fails at (iii), as it just propagates Java exceptions, but I don't think that is impossible to fix, so not a fundamental flaw. JVM is too heavy, and that is a problem for some. Otherwise, it's a well thought-out Lisp with a thriving community and some cool guys and a BDFL (i.e. Hickey).
Common Lisp excels at all the three of the items I listed, plus it's batteries included and has lots of libraries around. Also, it has a standard, so that you can develop on SBCL and deploy with Clozure CL or CMU CL. It's downside is there's some historical baggage and there are no DHH or Hickey or Torvalds in the community, which isn't a downside for me, even an upside.