Is T7 promotor leaky in DH5 alpha?
Consider the phenomenon of zygotic induction, as originally observed by Art Pardee, Francois Jacob, and Jacques Monod (sometimes called the "PaJaMo", or "PaJaMa" experiment): regulation of a repressed promoter can be affected by the copy number of the promoter in the cell. Put another way, if the copy number of the lac operator in the cell is high enough to bind or titrate all of the available lac repressor protein in the cell, then some of the lac promoters in the cell will be expressed.