The worst example of UI lag I've ever seen is on the shiny new treadmills they installed at my local gym a few years ago. While there are a few physical controls, most of them are now touchscreen-based. The speed-up and speed-down controls adjust the target speed, but the only visual feedback shows how fast the treatmill's currently running, and there's no indication of whether it's reached the target speed, which can take several seconds...
So a new user hops on the treadmill, leans on the speed-up button until it feels about right, lets go then hammers the speed down button in a panic as it keeps getting faster! Fun to watch, but a poster-child for how not to do UX!
The worst example for me is the volume knob on the radio in my car. When I start it in the morning I often find out that I was listening to something too loud last time I drove and I fruitlessly spin the knob for the ten seconds it takes for the radio to finish booting.
I think the digital version of the volume knob is a serious downgrade from the old analog version. It's probably cheaper though. The manufacturer saves $10 and I spend the next 5 years swearing at my car right after starting it.
So a new user hops on the treadmill, leans on the speed-up button until it feels about right, lets go then hammers the speed down button in a panic as it keeps getting faster! Fun to watch, but a poster-child for how not to do UX!