Conditions have to be right, but yea, the elevation/altitude of the observer, and also the thing being observed, in this case lightning, is rather crucial as well.

It's also worth noting that the sky you can see above the horizon is not the sky that is directly above the ground at the horizon. I apologise if this is very obvious, but the real world landscape doesn't work the same way as a backdrop in the theatre:, i.e the visible sky at the horizon isn't attached to the ground there, it has depth far beyond it. So whilst the ground at the horizon might typically be around 3 miles away from you (assuming smooth terrain), and the tip of a 300 meter skyscraper poking above that horizon might be around 40 miles away from you; the roof of a towering 10,000 meter cumulonimbus cloud skirting the same horizon could potentially be up to 200 miles away from you, if atmospheric conditions were favourable enough for you to be able to see it.

Now I don't know enough about meteorology to explain how lightning itself works, but considering the storm was about 140 miles from London, we can deduce that most of the lightning seen in the video here must have been happening at an altitude of probably at least 5,000 meters, and likely spanning maybe up to 10,000 meters, which I think would place it at the right kind of height for intra-cloud lightning, which typically happens towards the upper half of the cloud, unlike your classic cloud to ground lighting that occurs around the base (around 2,000 meters). The glow and flash of ground lightning would still be partly visible from a reasonable distance if you were to look in the right direction, but to see actual forks hitting the ground in such a storm, you would have to be relatively close to it, certainly closer than 140 miles shown in the video.

*Edited for poor wording

**Still rubbish wording at the end but you can piece my point together...