A lo mejor
 

Why is there an a in front of lo mejor?

A lo mejor is an idiomatic expression meaning maybe/perhaps.

me puedes decir
 

Why is the subjunctive of poder not used with a lo mejor? I'm thinking it's because Marsopa has no doubt that you can actually can help her, but if she did have doubt, then she would have used the subjunctive.
Is that correct?

I don't know if this answers your question about why it doesn't take the
subjunctive, but a lo mejor more often means probably which is close to perhaps but with a much more positive spin to it. Now that I think of it, perhaps (tal vez, quizás) doesn't take the subjuctive either.

Correct, if you believe what you're saying is true, the indicative tense follows a lo mejor/quizá(s)/tal vez. If, on the other hand, you aren't so sure, use the subjunctive.

Thanks , it feel good to be right sometimes, must be learning something.