The RTA function on the FMC is generaly pretty good if asked to achieve a solution within the parameters it considers realistic. The ATCO needs to have a ball-park idea of what is achieveable under the current conditions.
The following sounds cumbersome from both an FMC programming and a mental DR point of view:
I have heard people also say to adjust their (BULLA) pattern departure time to cross LIZZI at time xx
The following is easier from FMC and mental DR points of view:
Personally, I tell the aircraft to adjust their pattern to depart BULLA at required LIZZI time - 7 minutes.
I presume you do the maths for the them???
(XX:XX - 7min)
Remember, at this stage of the approach, many airlines' SOPs dictate less heads-down (ie FMC programming) time and more heads-up.
Personally I would prefer to be given time to depart the next waypoint I am due to cross. If it is during the hold, then it's easy to use mental DR to adjust the pattern so as to turn inbound to pass the next fix on time. Seems to work.
A good reason to have a pass in mathematics???
The FMC RTA (Required Time of Arrival) function works well over long distances and the Set Course time (or whatever it's called - for holding, etc) is something I don't usually bother with as I'd rather be looking out the window or otherwise maintaining SA, flying the airplane, etc.
PS: While we're at it - please no more "Descend at 250 knots", five seconds after we've nosed over at TopD!!!