RichThesaurus
on the lookout
vs
with one's eyes/open/peeled/skinned
on the lookout
prep
Constantly alert, intent on finding something or someone.
with one's eyes/open/peeled/skinned
How often have the words
on the lookout
and
with one's eyes/open/peeled/skinned
occurred in a corpus of books?
(source:
Google Ngram Viewer
)