Using light to launch an interstellar probe has a number of things going for it, but it's not all peaches and cream.
Most importantly. it's wildly inefficient in the short term. For a light beam bouncing off a mirror, the thrust applied to the mirror amounts to 150 MW of optical power per newton of force. Note that a newton isn't much. For the video's proposed 70 GW array, that amounts to about 467 N, or about 100 pounds of force. Of course, the advantage is that the thrust just doesn't stop. The linked video talked about sending a package to Mars in 8 hours, and this is correct. What you may not have realized is that the package under discussion is a CubeSat, and these things have a maximum mass of 1.33 kg. For such a light object, the acceleration is about 35 g's so yes, it really does get moving. Also note that nothing is said about how to slow it down once it reaches target. This is not, in principle, difficult: you just have another 70 GW array orbiting Mars which applies deceleration. It is unfair to ask how the target array got there in the first place.
So, there are (at least) 2 things to ask about an interstellar launcher. How big is the laser array, and how big is the probe? Let's say, just as a starting point, that the probe has a 1 $km^2$ light sail, and weighs 1000 kg. This is clearly not a manned probe, and the technology is beyond what we can do (if nothing else, we can't guarantee reliable operation for a century or more, and that assumes average velocities of about 0.3 c - more on that later). Let's say that the laser arrays are the video's 70 GW. As the video points out, solar power makes the most sense, especially for long-duration power production. Conceptually, each array consists of a 10 km x 10 km solar cell array which will orbit oriented to point directly at the sum. The back side of the platform is a phased-array of laser emitters producing a total of 70 GW, with a beam steering capability of +/- 60 degrees. This limits the illumination time for an object to about 1/3 of the array's orbit. Fortunately, you specified that 3 launchers will be built, so if the 3 arrays are in solar orbit at 120 degrees spacing, one will always be available for use. An obvious requirement in this case is that the array orbit must be inside earth's orbit, since the arrays can only fire outward from the sun.
With a probe mass of 1000 kg, acceleration will be nominally about 0.467 m/$sec^2$.
How long will the array be able to supply power? Assuming a 1 um laser wavelength, the diffraction angle for the beam is the Rayleigh criterion $$\theta = 2.44\frac{\lambda}{D} = \frac{2.44 \times 10^{-6}}{10^4} = 2.44\times10^{-10}\text{ radians}$$ and this will produce a spot size of 1 km at $$ R = \frac{d}{2 \theta} = \frac{1000}{2\times 2.44\times 10^{-10}}= 2\times10^9\text{ meters}$$ or about 7 light-seconds. After this range, the thrust will drop off as the square of the range, since the beam will get larger and large and the mirror will intercept a progressively smaller portion of.
The high-boost phase will take$$ t = \sqrt{\frac{2s}{a}}= \sqrt{\frac{4\times10^9}{.467}}=857,000\text{ sec}$$, or about 10 days and velocity at that point will be $$ v = at = .467\times 8.57\times10^5 = 4\times10^5\text{ m/sec}$$ I am, frankly, too lazy to do the math for the post-peak acceleration, but let's round up the final velocity to about $10^6$ m/sec. Note that this is only about 0.3% of c, and time to 61 Viginus is about 8600 years.
It's clear that we need bigger guns.
Now, as promised, the question of how to slow down at journey's end. It's very, very clear from the previous that there is no way affect the final trajectory with the specified array. It simply will not produce an appreciable power density over 30 light years. But let's say that we could, somehow, do this. Does that help? The answer is yes. During the voyage the probe turns around and ejects a second, much larger mirror which precedes the probe. The braking beam impinges mostly on the secondary mirror, accelerating it, but the reflected beam hits the probe mirror and provides a braking force. This is not exactly a friendly move towards the target system, since it produces an expended secondary mirror which whips through the target system at (for a secondary mirror equal in mass to the payload probe) about twice the transit velocity. Admittedly, the braking mirror is presumably some extremely lightweight material, but still...
Assuming a launch acceleration adequate to produce low-relativistic velocities, launch window is fairly forgiving, about 4 months/year. The immediate issue is to eliminate the cross-target velocity of the probe. Doing this immediately will, of course, result in a small radial velocity for any probe launched with a velocity near Earth's escape velocity, since the orbital velocity of the earth is about 30 m/sec. The ideal launch point occurs when the sun/earth vector is about 45 degrees to the target vector. Then the cross-target velocity is relatively small, and angling the mirror to eliminate this will also produce decent down-range acceleration. The exact optimum and window will depend on the thrust available and the launch velocity of the probe from earth. In principle, there is nothing to prevent using the laser beam to provide all of the thrust and the probe assembled in low earth orbit, but the numbers need to be worked out.
EDIT - Oh yes, and about the gravitational lensing thing. You can probably forget it. I haven't been able to get at the underlying calculations, but it seems pretty clear that the author simply doesn't know what he's talking about. A discussion of this is beyond the scope of this question, but I'm fairly certain that it won't work. His claims and explanations are to some degree self-contradictory, and he seems to have overlooked a few very important issues. I could be wrong (as history has shown) but I'm fairly sure I'm not in this case.
