Zero lash to me means that you reach a point in tightening down that you can no longer rotate the push rods.
With new hydraulic lifters that have never been run, some manufacturers recommend placing them one by one in a can of oil, submersing them and pumping them to load them with oil, then install them and adjust the push rods to zero turn.
Original Ford hydraulic lifters, you just bolt the rockers down as far as they go and that's it.
New ones will make a racket at initial start up without priming them, until they pump up with oil.
With the Ford system, that doesn't matter since they use a positive stop system that stops you from over tightening.
With aftermartket lifters, it is a different system. You really need to pre-prime them.
Another method with aftermarket lifters is that you can install them one by one, adjust them down according to the the rotor position in the distributor, which is the same procedure that you would do with solids. Then start the engine and let it run for a minute so the engine pumps up the oil in the lifters. Then go and do it all again to adjust for zero lash by tightening down until the push rods don't turn.
Personally I find this more work then using solid lifter cam shafts, since you are doing everything twice. I won't use hydraulic lifters unless I am just replacing individual lifters, push rods and rocker arms in an original engine. To me, that is what hydraulic lifters are intended for.
The other negative to me about hydraulic lifters is because they work by oil pressure, you never truly get 100% lift as spec'd on the card and the lift varies according to oil pressure, especially when you have changed the valve springs out to higher then stock pressures. There the higher rate springs are pressing more down on the oil pressure that the oil pump is producing.
At some point, the valve springs win out over the oil pump.
Is this confusing enough? I can work it more to make it worse?