Preheat the oven to 375 degrees F. Line a baking sheet with foil.
Cut the fennel into thick slices. Shingle them onto the center of the baking sheet and season with salt and pepper.
Zest 2 of the lemons and set aside, then juice these lemons into a medium bowl. Whisk the olive oil into the lemon juice and season with salt and pepper. Halve the remaining 3 lemons and add them to the bowl along with the potatoes and carrots. Toss to coat. Spread the vegetables and lemon halves around the outside of the baking sheet. Put the chicken thighs in the same bowl along with the reserved lemon zest and more salt and pepper. Toss to coat. Put the chicken on top of the fennel skin-side up, leaving a little space between pieces.
Bake, stirring the potatoes and carrots halfway through, until the chicken is cooked through and the vegetables are tender, 50 minutes to 1 hour. Serve the chicken with the vegetables and roasted lemon halves.