35 years ago, I always adjusted the mechanical-lifter valve lash on a running engine. For the past 10 years, I have adjusted valve lash with the engine not running. Of course, my limited experience is with 216/235/261 truck engines, which all came from the factory with mechanical lifters.
I find the engine-off method to be far superior: less messy, much easier to do, and less valve-train noise afterwards when driving the truck.
