In a large Dutch oven or heavy-bottomed pot, melt butter and olive oil over medium heat.
Add sliced leeks and a pinch of salt; sauté for 5 to 7 minutes until softened and translucent, avoiding browning.
Add minced garlic and cook for 60 seconds until fragrant.
Add cauliflower florets, diced potatoes, and broth to the pot; bring to a boil over medium-high heat.
Reduce heat to low, cover, and simmer for 20 to 25 minutes until all vegetables are fork-tender.
Remove from heat and use an immersion blender to purée the soup until completely smooth. Alternatively, transfer in batches to a standard blender.
Return the pot to low heat and stir in the heavy cream, fresh thyme, salt, and black pepper.
Simmer for 2 to 3 minutes to incorporate flavors, then stir in lemon juice before serving.