How can a continuous RNA be transcribed in the lac operon? The lac operon has 3 genes: lacZ , lacY and lacA. I have seen that the m-RNA transcript of these genes has stop codons in between. So, how can the RNA be made continuously? Won't the RNA Pol detach if there is a stop codon in between?

RNA Pol doesn't worry about stop codons. Transcription termination can occur through the formation of a hairpin in the new RNA sequence, or through the action of Rho proteins. A lot of the time prokaryotes have polycistronic mRNAs, that is, mRNAs with multiple protein coding regions. The stop codons are detected during translation, so you will often have all three lac proteins being translated at once off of the same mRNA.

Here's a nice section on transcription termination, or look up Rho-independent or Rho-dependent transcription termination for more info.