be lost in (something)

To be fully and deeply engrossed in something, such as a thought or idea, often to such a degree as to be unaware of or insensitive to the outside world. It's no use trying to talk to Helen when she's lost in thought like that—it's as if we don't even exist! I've been lost in this show all day and didn't even hear the phone ring when you called. Sorry, what did you say? I was lost in a world of my own there.

be ˈlost in something

be giving all your attention to something so that you do not notice what is happening around you: to be lost in thought/admiration