Once Karthus dies, his passive allows him to cast spells for 7 seconds. I'm curious how many times I can cast Lay Waste while still leaving enough time to cast Requiem. Since his CDR affects this, assume any CDR between 0 and 40 (max).
Requiem channels for 3 seconds, which gives 4 seconds of actual time to Lay Waste. Lay waste has a base cooldown of 1 second. Lay waste also explodes after .5 seconds (though karthus can cast other abilities while it's waiting to explode)
At a CDR of 0
With immediate reaction time, 4 lay wastes are possible, since each will have a 1 second cooldown. Immediate reaction time is not feasible, though, so let's call it 3 Lay wastes
At a CDR of 40
Lay waste's cooldown becomes .6 seconds. Meaning Karthus can get of 6 Lay Wastes in 3.6 seconds. This assumes, however, that there is no more than .4 seconds of total delay between Lay Waste coming off cooldown and being cast again. This is likely difficult, but theoretically possible.
after karthus dies, I can only use laywaste 2 times if I want to use R. If I am lucky, I can cast only 1 more spell after R finishes. Sometimes I cannot. I have tried to cast laywaste 3 times before I hit R. Most of the time, there won't be enough time. Actually I cannot recall any time I succeeded (3 Q then R). So my advice, laywaste 2 times at most then R. after that, you might be able to put a wall or another laywaste.