That might not be possible. This is because the pET vectors require T7 polymerase which is in the case of E.coli is integrated in the host (for example strain DE3). Also since your bacteria lacks the lac operon and lacI even if you were to introduce it on such a vector there a chance it would be lethal due to uncontrolled overexpression.

Check this reference: https://www.nature.com/articles/nbt0488-428. They have constructed multiple shuttle vectors that can be used for what you want and they cloned lacI on the same vector so that it is tunable (plasmid pEC701). Expression from plasmid of based on E.coli lacP.

Best of luck,

Hanna