What happens if there is a mutation in the Lacl protein gene?

Answer 1

The mutation would abolish the repressing ability of LacI and promoters controlled by it would be transcriptionally active in the absence of lactose. It could destroy or not do anything at all to the cell.

Answer 2

Lots of different things depending on the type of mutation and your system. In a simple case, the mutation would abolish the repressing ability of LacI and promoters controlled by it would be transcriptionally active in the absence of lactose, IPTG or any other inducer that binds to LacI and forces it to release DNA.

Another case would be that the mutation doesn't affect the DNA binding of LacI but the inducer binding ability. Then you could have a locked ON repressor that would keep the respective promoters silent regardless of the presence of inducer molecules.

You are not giving us any info so how do you expect us to give a specific answer?