Can a tenant sue for liability due to fire?

If you are in the United States then the answer is yes. Anyone can sue anyone else at any time for anything. It is your right.

However, if you are to have a chance of winning your case you will have to prove that the other party , your landlord was somehow negligent or directly responsible for the fire in the course of your loss.

Remember that since Tort Reform, if you lose your suit against your landlord you will be responsible for all legal costs. Yours and The Landords attorney bill, all court costs as well as any other damages such as punitive and lost income suffered by your landlord as a result of your suit.

Last but not least, this is probably more of a legal question than an insurance question.