Place garlic cloves in a food processor; pulse until minced.
Melt 1/4 cup butter in a small skillet over medium-low heat until slightly browned, 2 to 4 minutes. Add garlic; cook and stir until fragrant, 1 to 2 minutes. Mix lemon juice, canola oil, and sea salt into garlic mixture.
Transfer garlic mixture to the food processor; process until smooth.
Heat remaining butter in the skillet; add garlic mixture and simmer for 5 minutes more.