There are lots of factors to consider about noise from electrical storms. However to put it into perspective.

the power from a DSLAM is around 20dBm on ADSL. 20 dBm converts to 0.1Watts

A single bolt of lightning has 5 Billion Joules of energy (or more) that is dissipated in a few microseconds and that equates to something like 1 TeraWatt 1x10¹²12 Watts. Yes, it goes in all directions, however it only takes a minuscule part of that to hit your line and there is a nice little pulse of noise! Put in reflection and pick up at various points and suddenly your modem sees a loss of signal/sync.

50 to 100 miles - no problem in that sort of range ... 200 possible. Just based on gut feel and experience

To add to your interesting comments, back in the 1970s using early dial-up, I could tell readily when there were lightning storms in the Lake District about 150 miles away; and almost in the middle od about 350 miles of phone wire.