Oven to 425°. Spread 1 Tbsp olive oil over the surface of rimmed cookie sheet.
Run the potatoes through a mandoline or slice by hand to get 1/4" thick slices. Toss potato slices with 2 Tbsp olive oil and minced garlic. Salt and pepper to taste. Arrange the potatoes into 4 piles on the cookie sheet. Bake until brown in spots and just tender, 30-35 minutes.
Pat the mahimahi dry with paper towels and season with salt & pepper. Place 1 mahimahi fillet on top of each potato pile. Top with butter pieces, thyme sprigs and lemon slices on top. Return to oven and continue to bake until fish flakes when poked with knife, about 15 minutes.
Place one potato & fish pile onto each plate and serve!