Preheat oven to 150°F (70°C).
Heat oil in large frying pan.
When hot, add fish and cover; cook 3 minutes over medium-high heat.
Turn pieces over, season and drop in 2 fennel sprigs.
Continue cooking 3 to 4 minutes over medium heat.
Remove fish from pan and keep hot in oven.
Add butter to frying pan.
Cook remaining fennel, mushrooms and shallot 3 to 4 minutes covered; season well.
Add lemon juice, mix well and pour over fish.