Is RNA polymerase affected by proteins bound to the coding sequence of a gene?
Nice question!
First of all make sure that you have multiple transcription stop / terminator sequences at the end of your first gene . This is quite standard procedure. Also in your case the phenomenon called transcription interference (TI) comes handy. Here's a review on TI. In short:


  the term TI usually refers to the direct negative impact of one transcriptional activity on a second transcriptional activity in cis.


Although TI is mostly defined as two transcription events affecting each other, at the low level the basis of it is that two proteins bound to the DNA affect each other's activity. Now since LacI's function is to inhibit transcription, thus it is strongly bound to the DNA and I'd say even if a polymerase somehow slips through the polyA signals at the end of the first gene it is likely to be stopped by the LacI already bound at the second promoter.

Alternatively you could put a weak promoter opposing the first gene and drive its expression, so it would collide with the oncoming polymerase from the first gene thus stopping it before reaching the second gene. Also here is another article on TI, that proposes a gene regulation network based on TI.