Chez lacks a built in OOP system, but there is nothing prohibiting you from adding something like CLOS which does all python does and more (much faster than python).
Most modern lisp compilers do a lot of different things to make CLOS fast, though, prefilling caches and all that for you. Not only that, you can connect to a running program and redefine it while it is running.
In that case, the answer is actually no to my question. Yes, of course you could program in that level of dynamicness, because you could in any language, but it will then slow you down. No sensible CLOS would be as dynamic as Python.
Like I said, in a lot of ways, you don't want to be as dynamic as Python, and I advise against language advocates seeing the phrase "Python is more dynamic than your language" as a cue to jump up and start insisting that they are just as dynamic as Python. Even in hindsight, I'd say the level of dynamicness in Python was a mistake. You don't need it to have a nice, usable, dynamic language, but it has been a ball & chain around its legs in terms of performance for decades.
To be clear, this isn't a criticism of dynamic languages as a concept. I have criticisms, but these aren't it. This is a criticism of Python specifically. A dynamic language can be pretty nice with, let's say, two or three layers of dynamicness, but Python has four or five. If you follow the full process that Python has to go through to resolve "x.y", including all possible points where you might have done something to affect the result, it's crazy overkill. In Guido's defense, when he was writing it way back when, that wasn't clear. There wasn't a lot of highly-relevant prior art to look at for that style language.
CLOS is just as dynamic as Python _and_ fast, at least in SBCL and LispWorks. CLOS is probably the most expressive object system you can find, and if you wanted it fast you would restrict it somewhat to allow for at least some of the dispatch to happen at compile time :)
Most modern lisp compilers do a lot of different things to make CLOS fast, though, prefilling caches and all that for you. Not only that, you can connect to a running program and redefine it while it is running.