To pick up EM radiation caused by lightning strikes I use a round ferrite rod
(about 4.5 cm long), with about 400 turns wire, tuned with 150 pF in parallel
to about 40 kHz.
Finally got some lightning, woke me up at 5 in the morning, took me some
minutes to get it together to go get an oscilloscope and do measurement.
By that time lightning was far away, outside I could see the flashes,
but not even hear the sound anymore (so could not time the distance).
But on the LW receiver (150 kHz) the cracks were clearly audible.
I measured < 10 mV noise on the ferrite rod without lightning.
Measured > 30 mV pulses of about 2 ms duration of 40 kHz each time a flash
happened.
Maximum pulse hight measured about 50 mV (for these flashes far away).
Went back to sleep.

So, it should be possible to use a simple PIC 12F629 microcontroller
( www.microchip.com ) as a pulse detector (these have an analog comparator)
at a slice level of about 20 mV.
The processing to discriminate between other signals and the lightning
induced ones, and generation of a 1000 Hz alarm tone for a piezo beeper can
then be done in software.
Some silicon diodes parallel to the LC antenna should limit and protect the
PIC for nearby signals...
3V (2 AAA batteries) should be enough to power the thing for a long time.
Add an optical alarm LED.
Tested with the ferrite rod horizontal, with the rod's axis pointing towards
where I did see the flashes, and also with the rod vertical.
In theory vertical should be better.
Both configurations worked, however I did not get enough flashes to be able
to try to 'zero' the signal by rotating the rod.