线上看 is like 街上看(熱鬧), where 线上, like 街上, serves as an adverbial of place.
上线看 is like 上街看(熱鬧), where 上线, like 上街, serves as a verb phrase.
看在线(好友) is like 看在家(老母), where 在线, like 在家, functions as an adjectival modifying a noun (好友, 老母).
在线看 is like 他在家看(電視) "He is at home watching TV", where 在线, like 在家, functions as a predicate adjective.