Soak sweetbreads in a large bowl of water for 1 hour; drain.

Place sweetbreads in a saucepan and cover with cold water; bring to a boil. Drain. Run cold water over sweetbreads to cool.

Return sweetbreads to the saucepan and cover with cold water again. Add 1 tablespoon butter, lemon juice, and salt; bring to a boil. Simmer for 10 minutes. Remove from heat and let cool.

Melt 3 tablespoons butter in a heavy-bottomed skillet over medium heat. Add mushrooms; cook and stir until tender, about 5 minutes. Transfer to a plate.

Melt remaining 3 tablespoons butter in the skillet. Add flour; cook and stir until a paste forms, about 1 minute. Season with paprika and cayenne. Pour in milk slowly, whisking until sauce is smooth, 3 to 5 minutes.

Stir sweetbreads, mushrooms, and peas into the sauce; cook until peas are heated through, about 5 minutes. Season sweetbreads with salt. Serve garnished with jalapeno pepper.