Probably in excess of 60%, the warmer, breezier, and more humid the better.
These plants have the potential to get huge, and definitely not a terrarium plant. The individual leaves can be 18" long.
One of my 2 echinolabium came from a friend who grows vandas (very well). He had it for about 3 years, and it never bloomed, and the largest leaf was only 10" or so. He grew it outdoors in the summer, and brought it indoors in the winter. Summers in TN can be pretty hot/muggy with 70+% humidity, but indoor winter conditions are fairly dry without controls, and probably averaged around 40% for him.
In my GH with >70% humidity year round the plant took off and started producing 16"+ leaves, and flowered within the year.
So while they can take drier conditions, you will get faster/better results in more humid conditions.