Cook the bacon in a medium saucepan over high heat, stirring frequently, until just brown, 2 to 3 minutes. Add the onion and garlic, and stir constantly until fragrant, about 1 minute. Add the wine, bring to a boil and cook, stirring, to scrape up any bacon and browned bits, for about 1 minute. Stir in the lentils, chicken broth and pepper flakes, and return to a boil. Cover and cook, stirring occasionally and reducing the heat if necessary to maintain a medium boil, until saucy but not watery, about 3 minutes. Remove from the heat, and stir in the celery, celery leaves, 1/2 teaspoon salt and a few grinds of pepper.
Season the fillets all over with 1/2 teaspoon each salt and pepper. Heat the oil in a large nonstick skillet over medium-high heat. Once the oil shimmers, add the fillets skinned-side down and cook, undisturbed, until crisped and browned, 3 to 4 minutes (the fish should be opaque between the large natural flakes). Flip the fillets, and cook until just beginning to flake, 1 to 2 minutes. Remove the fillets from the skillet, and turn off the heat. Add the butter to the skillet, and allow it to melt and brown.
Divide the lentils among 4 bowls or soup plates, top each with a fillet and drizzle with browned butter.
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