Prepare a grill fire to 300° using oak or pecan for smoke flavor.
Pat chicken pieces dry with paper towels. Coat lightly with olive oil and season with salt and pepper.
Cook over indirect grill fire with the lid closed for about 8 minutes.
Turn the chicken and continue to cook until internal temperature reaches 160°, chicken will continue to cook in the sauce.
Remove from grill and set aside while you make the sauce.
Slice mushrooms, dice onions and mince garlic.
Melt butter in a large skillet over medium heat. Add the onions and garlic, stirring often about 2- 3 minutes.
Add the sliced mushrooms, stirring occasionally until mushrooms are softened and start to caramelize.
Stir in chicken broth, heavy whipping cream, Worcestershire sauce and dijon mustard.
Whisk in lemon juice, salt and pepper.
Add the chicken pieces and continue to cook, stirring occasionally about 5 minutes.
Turn chicken pieces, cooking another 5 minutes until sauce has reduced slightly.
Serve chicken with sauce spooned over the top.