They are not related any more than English "mare" and "square" are.
Лошадь is believed to originate from Turkic languages.
Площадь is a native Russian word, ultimately from a Proto-Indo-European etymon, which is also a distant ancestor of the English word "flake".
There are lots words in Russian. For purely statistical reasons, ...
I would like to add, that the recent meaning of "лихой" more like - causing a great effect, and not always in a positive way. For example: "Это был лихой день" means that the day was full of events that causing a great effect, good or bad depends on a context.