Yes the Listerine definitely helps the itching.
I have never clipped a horse that had lice- with one exception and that was not a Mini and was so bad it was life threatening.
In that case the lice were so big we actually clipped through some of the bodies so the animal had also to be on antibiotics in case of infection.
One of my Arab mares got lice in the last month of pregnancy and I used an old, OLD remedy.
You put grease (pig fat was suggested but I actually just used Lard) along the back from behind the ears to the base of the dock.
Then a ring around the anus and the neck.
Lice and fleas, apparently, get moisture form the eye and the anus of the host.
The lice also swap sides of the host once a day.
To do either they have to pass through the thick line of grease- they bury their heads in this and suffocate and fall off.
I only used it the once- the lice of this mare were so bog I could see them without any help at all- and they were all gone, completely and without any chemicals or clipping, inside of 24 hours.