Unlike Reesha, I have never particularly cared for bechemel in lasagna. It's often just too heavy and rich for me--and I don't generally shy from rich foods. I have to wonder if all that cheese will overpower the mushrooms.
That said, here is an alternative to the NYT's recipe that goes a little easier on the cheese. It also looks to be a bit cheaper to make (which is often a concern of mine). I'd be tempted to try this one notwithstanding my prior comments because I know DH would love it.
Live with intention. Walk to the edge. Listen hard. Practice wellness. Play with abandon. Laugh. Choose with no regret. Continue to learn. Appreciate your friends. Do what you love. Live as if this is all there is.
--Mary Anne Radmacher