Hanks was reading a very interesting book,and he was completely lost to the outside world.
非谓语动词作状语表示伴随,非谓语动词作状语要省略be,故为completely lost to .表示一种状态.
be lost in sth.沉迷于.如果你用losing 可以这样改
Hanks was reading a very interesting book,losing himself to the outside world.