Curious issue with Lasso tool.

I sort of think of the lasso tool like the direct selection tool, but with more flexibility in how it selects objects. But there is an important difference and it might be a flaw.  The lasso tool selects objects that are masked inside other objects.  The direct selection tool does not.  The box has horizontal lines masked inside but if the lasso passes over those lines, it will select them.  Look at the screen shots.  I have some art which is like this, but more complex.  It seemed like a perfect job for the lasso tool, but all of the hidden elements from another object are being selected.