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What are the chances of detecting gravitational waves from a supermassive BH merger within a lifetime?
Quite good, actually! The expectation is that LISA will be able to detect a few 10s or 100s of massive black hole coalescence events per year.
Massive black hole binaries result from galaxy mergers, as the central black holes find each other and spiral together pretty rapidly (within about 100 million years). It has been a problem though to understand how, once they get to about 1 parsec apart, they manage to continue to spiral together to merging. At distances much greater than 1 parsec the inspiral works efficiently by scattering stars, yet gravitational wave emission doesn't become too strong until scales much less than 1 parsec. So for a while astronomers did not understand why we do not see large numbers of black hole binaries "hung up" with ~1parsec separations -- the "final parsec problem"
Lately this problem has been pretty much resolved, and it turns out there are actually several mechanisms that allow the inspiral to proceed all the way to coalescence. Not only is that good for our understanding of mergers, it also means we are very likely to see the process in gravitational waves. The entire population of massive black hole binaries in the universe produces a stochastic background of gravitational wave noise, which should be detectable in Pulsar Timing Arrays. At least one of these systems should be nearby and massive enough to resolve individually above that background noise, as well. What is the actual coalescence rate across the universe? Estimates vary by author and model, but optimistically it may hundreds per year out to a redshift z=5, and pessimistically still about 10.
To interpret this figure, think of it as showing the number of events you expect to see per year, if you look out to a distance where the redshift is z, but happening within 1 unit of z of that distance. So for example if you want to know how many total merger events there are per year within z=5, then you would add up the number in each z=1 interval out to z=5, which for the left figure is nearly 1000, and for the right image is 9 (model I) or 15 (model II).For perspective, the comoving distance to a redshift of z=1 is about 3.3Gpc, and the comoving volume within that distance is 150 Gpc3. For a redshift of z=5, the comoving distance is 7.8Gpc, and comoving volume is 2000Gpc3. So we could infer that the rate in the universe today is something in the realm of 0.01 to 0.1 mergers per year per Gpc3.