Theory: As you probably know, HoT heals when/whilst the user has not taken source of damage, when the user is under the False promise Debuff, the damage is being considered but the HoT is healing the lion faster than the axe can kill.

The heart is healing the lion, whilst at the same time not being disabled by the damage caused by axe "If damage is taken from an enemy hero or Roshan, this ability is disabled for 5 seconds for melee heroes, or 7 seconds for ranged heroes.".

For False Promise: "Any healing that is delayed by False Promise is doubled." therefore delaying and doubling the healing done by HoT. Perhaps is healing more than the axe can deliver in damage? HoT is not being disabled by axe during False Promise because the ULTI blocks direct damage until the debuff ends.

I believe It is working correctly, but that is a nice interaction could be bug shrug

Example: Oracle uses false promise, Hit, Heal x2(delayed), Hit , Heal x2 (delayed), Sun appears , Lion has only taken small damage.