I discovered three interesting episodes of The Food Programme on BBC Radio 4 the other day via a link I saw discussing the episode about running on LCHF which included an interview with Tim Noakes.
All three episodes discuss the topic of eating for running and cover things like the traditional high carb diet, vegetarian diets, what the east African's eat and finally the third in the series covered LCHF.
No definitive "best diet" decision was made, but it was interesting to hear the discussion about the different diets and the research behind them.
All three episodes can be found at https://www.bbc.co.uk/programmes/b006qnx3/topics/Running if you're in the UK. I did find versions on YouTube but they seem to have been removed now.