In OP's context, preoccupied is the better choice.
The pre- prefix implies already, which by further implication suggests there's something else that Lenny should be doing. Being "occupied" usually implies doing something meaningful / productive, whereas being "preoccupied" often means doing or paying attention to something relatively pointless (daydreaming, watching squirrels, etc.).
From WikiDiff...
As adjectives the difference between occupied and preoccupied is that occupied is "reserved, engaged" while preoccupied is "concerned with something else; distracted; giving one's attention elsewhere".
Here's an interesting chart showing how usage has changed over time in this area...
...where it seems unlikely that the real-world nature of introspection / contemplation / daydreaming would have changed all that much over the past century. So I think you can take it for granted the difference between these two words isn't as clear-cut as some people might like it to be.