This is the 12898th most frequent Russian word.
лезвию
"Лезвию" is the dative case form of "лезвие," meaning "blade" in English.
In this instance, 'лезвию' is used metaphorically to describe a precarious situation, in the dative case as part of the prepositional structure.
Прими осторожность, ведь ты ходишь по тонкому лезвию.
Exercise caution, as you are walking on a thin edge.
Here, 'лезвие' is in the nominative case, serving as the subject of the sentence.
Это лезвие мне больше не нужно.
I no longer need this blade.
Here, 'лезвием' is used in the instrumental case to denote the tool used for cutting.