Brother-in-law passed away but has a pending lawsuit and now his widow/my sister wants to continue lawsuit on his behalf. Is she considered the executrix of his estate and can act on his behalf?

Did he designate her the executrix in his will? Have her get together with the attorney who is handling the case for her husband.

She is, if the will appointed her, or if the probate court appointed her.
If not the person appointed by the will or the probate could would.
Now as his wife, if this was a personal suit, she may have a standing as such. But that would depend greatly on the terms of the suit

In New York, and I would assume similarly everywhere, you have to apply for Letters of Administration to be in a position to continue the suit. A wife is someone who would have first dibs on the position in most circumstances, but anyone who is appointed would have standing to continue the suit as the appointment places you in the shoes of the deceased Plaintiff.

The sad thing however is that when a plaintiff dies, so does any prosepct of recovering future lost wages and pain and suffering. So the value drops significantly.