I was about to teach you history, but I see you know about it .
Hot lime was used in the 18th century simply to match the explosive demand for the growing metropolis,where slaked lime was thrown trough screens to remove unslaked lime.its a simple process, less labour intensive and time consuming,which had to be back then. Hot lime will be the last thing I'll be using today for render and plaster. Mature lime putty is way better and will give you better results and finish.
Saying that, hot lime has also its advantages. In some circumstances hot mortar is advantageous-building with hard , impermeable stones, especially in cold, damp conditions,very little water is absorbed by the masonry, so building can be slow do to the risk of slumping.Hot mortars encourage evaporation and initial stiffening of the mortar.The heat is believed to improve the bond between sand and lime and may also activate some pozolanic content in the sand.Hot lime was common for foundation and core filling, but also for cold weather works.The ratio is 1:2;1:1.
I would suggest you take down the existing plaster and replace it with lime putty, or if you fancy hemp lime. The hot lime has cracked like spider net and is not reliable. To make things worse- you have used two different times of limes over each other! You can't make this up!