Heat ¼ cup oil in a large heavy bottomed pan on medium heat.
Arrange prosciutto in a single layer in the pan and cook until crisp, turning as needed, 5 minutes. Place on paper towels to drain.
Heat remaining 2 Tbsp. oil in same pan over high.
Cook mushrooms until tender, 8 minutes.
Reduce the heat to medium-low and add the garlic, shallots, and 1 tsp. thyme.
Season with salt and pepper to taste, stirring often, until shallots are translucent and softened, 2 minutes.
Add stock and reduce heat to low. Bring to a simmer and cook until only a thin layer of stock coats bottom of pot, 5−7 minutes.
Toss in the shredded chicken and mix.
Cook pasta in a large pot of boiling salted water, stirring occasionally, until very al dente, 3 minutes less than package directions.
Transfer the fettucine to the pan and add 1 cup pasta cooking water.
Crumble half of the crispy prosciutto into the pan and increase the heat to medium, tossing constantly, until pasta cooked to al dente and sauce is slightly thickened, 2 minutes.
Add the heavy cream and cook for an additional minute.
Remove from the heat and mix in the butter and lemon juice until fully incorporated.
Top with the remaining crumbled prosciutto and serve.