If an instrument like LSST quickly spots something as soon as it reaches magnitude 24½, how far away would a 60km first-time visitor from the Oort cloud be when it is spotted? I'm thinking that a huge iceball will make a visible coma sooner, but have no idea what actual numbers would be.
And, given that distance and a parabolic orbit, how much time would that give before it crosses Earth's orbit?
Even 100 meter NEOs could cause significant damage, and there are far more of them. LSST will be able to detect objects as faint as 24.5 in magnitude in a 30s visit, enabling it to detect 140m NEOs as far away as the Main Belt asteroids. [...] During its survey of the sky, LSST can find 90% of the PHAs over 140 meters in diameter.
Earth is 1 AU from the Sun, so that would be 1.2 to 2.2 AU away from us:
The Asteroid Belt is located in an area of space between the orbits of Mars and Jupiter. That places it between 2.2 and 3.2 astronomical units (AU) from the Sun. The belt is about 1 AU thick. The average distance between objects in the Asteroid Belt is quite large. If you could stand on an asteroid and look around, the next one would be too far away to see very well.
Timewise, it would be about 8 years away:
The bottom right panel shows an example of a very different hazardous object - the 3 km large comet C/1996 B2 Hyakutake, which passed within 0.10 AU from Earth in 1996. The apparent magnitude vs. distance diagram indicates that the current generation of wide-angle imaging surveys, such as SDSS with V < 22, could have provided an early warning about 3 years before the closest approach (if they had sufficient cadence and sky coverage). With LSST, the warning time would be ∼8 years, with over 500 observations over that period.
Fortunately, your comet is 60 km, making the comet tail easy to spot:
While the solid nucleus of comets is generally less than 50 km across, the coma may be larger than the Sun, and ion tails have been observed to extend 3.8 astronomical units (570 Gm; 350×106 mi).
This table of impact risks shows that the most likely (5.8e-02) impact is between 2095 and 2113.
