Hi Kis,
Here's my .02. You don't have to play by the ORG's rules. That's THEIR problem. This lady believes in you as a person, not as a JW, you see? You are her friend. She wants you as a person to say that prayer for her. I would have NO bad conscience about doing so. If there is truly a loving God up there, I can bet he would listen to YOUR prayers alot quicker than he would listen to the hypocrites who would dare to condemn you! My sympathies in the loss of your dear friend, btw.
Big hugs,
RCat