Why not this: Yo lo buscaba por todas partes. (imperfect tense)?
Imperfect means it happened in the past only. As written, the action is continuing into the present.
Why le instead of lo?
le is often used instead of lo; it’s called leísmo.
English Original Sentence
I’ve been looking for it everywhere.
In fact, using le (him) for an inanimate object is not proper Spanish; it should be lo. I can say that even though I’m not a native speaker.