How many channels of control do you need?
I’m not sure about LED drivers that take an IP control connection directly, but there are converters to 0-10V from Art-Net or sACN (entertainment lighting control protocols):
http://www.dfd.com/e8anl.html. Art-Net is a fairly simple protocol to implement, sACN is also not hard to implement but is documented in an annoyingly complicated way. There are open source implementations out there for both. There are probably some boxes out there, meant to be installed in walls to control architectural/house lighting that with a couple of slide pots that can send Art-Net/sACN, but I don’t know of any offhand. I’m sure there are also architectural lighting control solutions that could work, but most of those are designed for very large installations and likely to be cumbersome for only a handful of channels.
I think “Field I/O” is the term you’re looking for for off-the-shelf IO-over-IP. There are a few options here, they’re not cheap, at least until you consider the engineering cost of building something like this yourself as a one-off:
https://www.automationdirect.com/adc/shopping/catalog/field_i-z-o#start=0Alternatively, the Click series of PLCs are incredibly cheap for their capabilities, and they have models with Ethernet and analog IO included in the base unit, no extra modules required unless you need more channels. This looks like the cheapest approach, and would probably be the easiest way to get the physical knobs you want, not to mention you have a lot of options for additional functionality. You’d just need one of these at each end with a simple program to read the analog knob values and send them from the control PLC to the output PLC—the output unit might not even need to be programmed if its output registers can be directly written via MODBUS / MODBUS TCP:
https://www.automationdirect.com/adc/shopping/catalog/programmable_controllers/click_series_plcs#start=0&Item_Type_ms=%22PLC%22&Series_ms=%22CLICK%20Ethernet%20Analog%22