"Over" is a disposable word. If you omit it, the meaning does not change. "Over serves the same function as "there" or "yonder" to emphasize the distance or journey to the lake. "Found it out" = "revealed it" (I do not know how or why the road would reveal "what it would be like" but that is what the sentence says.)

On the journey from my home over to the lake I think it means because there was a proper road to the lake, then many other people will have discovered it too, and it would be very busy