Most lathes preview the a digital file which allows the lathe to cut within its safe parameters. All analog cuts that turn out great might be "minor miracles". I'm sure @atmasphere can explain the preview process better.
The preview process is simply looking for the quiet and loud spots so you can speed up the lead screws that drive the cutter head so as to prevent over-cutting (overwriteing a prior groove) and also so as to take advantage of space that is possible when the music is quiet.
The 'preview' can be done several ways. One way if you have a reel to reel machine is to place a tape head about 2 seconds upstream from the playback head- this head is often referred to as a 'digital preview' head because its output is used to digitally create the correct speed for the motor driving the lead screws. The Compucut system made in the 1980s used this technique.
You can also create speed information by playing the project first and then playing the speed file back while synchronized with the actual audio. That is the technique we used.
There are other techniques as well.
The reason its harder to do an analog master tape is the tape does not have normalization like is often found with digital source files. Its important to understand that an LP mastering lathe is almost impossible to overload. IOW the cutter head can easily cut grooves that no cartridge has a hope of tracking. So you have to be careful to not exceed playback limits. Especially if you are not using compressors or limiters this can be tricky and may require a bit of engineering time working with the project doing test cuts to see how problem areas work out.