I'm short on time, but I don't think there is anything wrong with giving your W a heads up.
Perhaps talk with your L first to see where you stand and then talk to her.
There is a fine line between DBing and then just doing what you believe is right. You seem to have a positive relationship with your W. I think I would let her know.
Just a very humble opinion...
BITS
Happiness is not something ready made. It comes from your own actions.
