First, are you sure your dimmer is Z-Wave? Lutron uses a proprietary wireless protocol in (almost?) all their products (e.g., the popular Caséta products use Clear Connect, which Hubitat interfaces to over Ethernet via telnet and other third-party integrations either do something similar or use the Lutron cloud).
If your switch is Z-Wave, some have a parameter or other option to disable the actual relay that turns the connected load on/off (e.g., I know Inovelli does but Zooz and others might too), which can basically turn it into a "smart button" of sorts that you can then make Hubitat do anything with--say, dim the lights (though how this works really depends on what events the switch reports to Hubitat--press, hold, release, etc.). I'm not sure the in-wall Lutron switches can do this (I don't have any). However, if you're using a Pico remote (which I do have), you can make it do whatever you want in Hubitat, including working like a dimmer, since every button is just something you can configure however you want in Hubitat (again, I don't have any of their hardwired switches so maybe they can do the same, but I suspect they are really just hard-coded to control the connected load).
That being said, the second part of your question involves "the dimmer updating its state." I'm guessing you mean your dimmer switch has some sort of LED "level" indicator. This is a bit trickier since (and again I could be wrong) I think the Lutron wall switch can just control the load, which with a Hue bulb is something you'll want to avoid doing with a dimmer switch (or at least the dimming).
If it were me, I'd probably ditch the wired dimmer and just use Pico remotes everywhere I want a dimmer (if you have Caséta or another compatible system, since it's not clear to me what you have). They fit in a standard wall plate, though you'd have to get rid of the switch underneath (or you can mount it standalone nearby or add an extra/empty gang). If you really like the wired switch, you might be able to find one that can be wired, has indicator lights, and allows disabling the relay so it doesn't dim or switch the mains power to the bulbs, but I'm not sure of any that meet all that criteria (if it weren't a dimmer or you know it's the type of dimmer that would work with this, you might also be able to make on that doesn't have a built-in relay-disable feature effectively work that way by connecting line to load behind the switch--and the smart switch will likely at least need line connected but I'm not sure what you'd do about load--or if anyone has tried this with a smart dimmer to see if it actually works; I'd not try unless you can find someone who knows more and has tried ). If you get the wired dimmer to work like this without actually directly controlling the mains power to the attached load but still able to "think" it's dimming, you could then have an automation that matches the smart bulb dim level to that of the switch in either/both directions when one changes, thus achieving your goal.
But Pico remotes everywhere and no hardwired switch (especially a dimmer) with smart bulbs would definitely be my recommendation if you have the Lutron Smart Bridge Pro. (If not, Hubitat is compatible with a lot of button controller devices that you can make to do something similar--and if your bulbs are Hue and paired to the Hue bridge, consider also the wireless Hue dimmer switch paired to the Hue hub.)