周囲 and 包囲: surrounding space and an encirclement
Compare a walk around a lake with a castle's encirclement in a story, distinguishing the surrounding place from the event.
The surrounding place in 周囲
周囲（しゅうい） means surroundings or the area around something. 「湖の周囲を歩いて一周しました。」 reports walking once around the lake. 湖の identifies what the surrounding area belongs to.
一周しました states that one circuit was completed. Walking around the lake does not describe besieging it or blocking access.
The event of 包囲
包囲（ほうい） means encirclement or siege. 「物語では城が四方から包囲された。」 says that, in the story, the castle was surrounded on all sides. 城が gives the target, and 四方から the directions of encirclement.
包囲された presents the castle's encirclement. It does not identify who surrounded it, whether escape was possible, or which passages remained.
The role of a place and an event
The 周囲 example locates the walk around the lake. The 包囲 example presents the event of surrounding a castle. A shared notion of being around something does not make their sentence roles identical.
Encirclement on all sides does not establish obscured visibility or that every form of entry was impossible. The surrounding place and the event concerning a target are read separately.
Does 湖の周囲を歩いて一周しました。 state that the lake was besieged?
Show the answer and why
No. It reports completing a walk once around the lake. It does not present an encirclement event such as 包囲された.