"Limerence is a state of overwhelming and unexpected longing for emotional reciprocation from another human, known as a limerent object..."

"... who is often perceived as perfect but unavailable.... The LO is most often a friend, colleague, or stranger met in passing... 'It’s often not romantic or sexual in nature. It is very much about wanting to feel loved and cared for.'... We begin to mistake anxiety for excitement and excitement for joy.... One strategy... to de-idolize their LO is listing reasons the LO is not perfect... [or the] ways in which the LO and the patient are not compatible. Name it to tame it: You can deliberately interrupt the habit by calling it out — 'Hello, limerence' — and paying attention (for example, through journaling) to what it feels like when you’re in that state of longing.... You should also believe you deserve more...."

From "Is It a Crush or Have You Fallen Into Limerence? How an intense longing for a romantic connection can lead to a serious addiction" (NYT).

The article says the word "limerance" was coined by the psychologist Dorothy Tennov, and the OED finds her first use of it in print in 1977. 

That first quote denies any etymology: "I first used the term ‘amorance’ then changed it back to ‘limerence’... It has no roots whatsoever. It looks nice. It works well in French. Take it from me it has no etymology whatsoever."

So if you were seeing a connection to "sublime" or "limn," just forget about it. If you can't forget it, make a list of things that are rootless, nice looking, and well functioning in French.