How many times can Karthus cast Lay Waste before casting Requiem after he dies?

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.