The best way to pick up lightening is to use a long exposure.
I would use either an SLR or a decent compact with manual controls.
Lightening is very very fast so you have next to no chance of timing your shutter release to catch it.
Get a tripod, set the lowest iso rating, set the smallest aperture (higher number) and set the shutter for a minute.
If the image is too bright set it to 30 seconds, if its too dark set it to 2 minutes etc until you get a good ballance.
When you get a half decent camera try and get one that accepts filters.
Add a polariser ot allow even longer expsoure times.
You really want a camera with manual control.
If you want video then select manual focus set it to infinity, expose manually, underexposing the sky by around a stop for contrast, and just let it run (have it under a proch or through an open window, do not leave your camera outside in a thunderstorm!!!!
Phones are great for fun, if you want decent footage, you need to use a decent camera.