I just stumbled on this with a Google search and I have to disagree here. I believe it could be done safely if the system were designed correctly.It wouldn't be Lithobraking anymore then, would it?
It would still make a great stunt at any lunar "air"-show, though...
The concept exists, but it would have to be a very long accelerator if you want to do it with maned craft.
Also, the needed precision is enourmous. And a failed landing would be a pretty big catastrophy, not only destroying the craft, but also large parts of the accelerator. And there's no touch-and-go if you mess up your first aproach.
The problem is the assumption of the low point in the orbit being just below the surface. That would make a spectacular mess if it went bad but it's not necessary to make the concept work.
Instead, make the approach orbit at all times clear the surface. Use multiple orbits to ensure the lineup is perfect. You make the first flyby well above the runway, the instruments there get a very precise position and so you know exactly how much velocity must be shed. Shed much of this and repeat. You can take baby steps down until the orbit is only a few meters above the runway.
At this point the sled is launched. The approach part of the runway is configured to almost perfectly match the orbit an approaching spacecraft is in, thus the sled will be moving at a very slow speed relative to the spacecraft (other than the fact that it's riding magnetic rails it's actually in orbit.) It reaches up and grapples the spacecraft and pulls it down and then slows it.
Up until the point that the sled grapples the do-nothing approach is always safe. After grappling you can still disconnect the grapples safely. You're only committed after the sled starts tugging.
As others have said the runway must be huge.
Note that you can take this idea to an extreme for efficient interplanetary transport. Consider what happens if you build the track all the way around the equator and design it to hold onto craft that are traveling above orbital velocity.
If I haven't blown the math somewhere you can accelerate to a transfer orbit to any point in the solar system (including escaping with several miles/sec) with no more than 5g's.