It's any Denon HDMI model number under the 3000 series. So, any 28xx or any big box store model (789, 889, etc). [big box stores don't have the 4-digit Denon models, even if some models are 'identical' to a corresponding 3 digit model] Example a AVR-3808 is a model you'd want to avoid, as is a 5808. 2809 and lower is good. So is a 789, etc.
From the 3000 series and up, the Denons have a menu GUI that overlays on top of HDMI sources, which means the signal is being processed. That's a no-no. This idea extends to other brands, so look for any receiver that can't overlay info on top of HDMI (volume control display, settings, etc) input. Some see this as a 'defect' I say it's the best thing ever! Usually higher-end models of a brand feature HDMI overlay, and you'd need to avoid those models. Some receivers even have Reon VX or Realta processors, which are perfect for those looking to double their lag
I personally have a Denon AVR-2809CI. It is 100% lag free in every way. I joined AVS only to find my magic equipment, and so far so good
There are no settings to adjust for HDMI. For analog sources, set the "Upscale" option to OFF, which is the default. [it can convert analog to HDMI as a feature]