PreparationFor lemon aioli: Whisk egg yolk, garlic, and lemon juice in a medium bowl. Whisking constantly, drizzle in vegetable oil, then olive oil in a slow, steady stream; whisk until aioli is emulsified. Season with salt and more lemon juice, if desired. Cover; chill. DO AHEAD: Aioli can be made 1 day ahead. Keep chilled. For mussels: Heat oil in a large heavy pot over medium-high heat. Add onion, season with salt and pepper, and cook, stirring often, until softened, about 5 minutes. Add garlic and cook, stirring often, until fragrant, about 1 minute. Add tomato paste and cook, stirring, until it begins to darken, about 2 minutes. Add wine and bring to a boil. Reduce heat and simmer until liquid is slightly reduced, about 1 minute. Add mussels and 1/2 cup water to pot, cover, and reduce heat to medium. Cook, stirring occasionally, until mussels open (discard any that do not open), 10-12 minutes. Ladle mussels and broth into shallow bowls and top with thyme; serve with bread and lemon aioli.