Look into my eyes, can't you see them walking by

Would I lie to you baby ? Would I lie to you ?

The story:

This song came out when I was in my early teen years and I loved it. I never really thought about the lyrics I would just kinda sing what I heard. I was singing this song one day and my older sister (who at the time I thought was so cool) called me out on my mistake. She said "that doesn't make any sense, how can eyes walk by"?