For any given digit range the numbers with the longest spelling have the highest LH.
7-only-combinations are always among those numbers. Here's a table with their corresponding LH:
number from here | number segment | letters from here | LH ------------------+----------------+-------------------+------- 777777777 | seven hundred | 87 | 9 2/3 = 9 14/21 77777777 | seventy | 75 | 9 3/8 7777777 | seven million | 68 | 9 5/7 = 9 15/21 777777 | seven hundred | 56 | 9 1/3 77777 | seventy | 44 | 8 4/5 7777 | seven thousand | 37 | 9 1/4 777 | seven hundred | 24 | 8 77 | seventy | 12 | 6 7 | seven | 5 | 5
Looks like 7777777 beat my previous suggestion. It worries me that LH(8878878) is the same (alongside others like 3878373).