Place 2-1/2 cups flour in a large bowl. Make a well in the center. Beat eggs, water and oil; pour into well. Stir together, forming a ball. Turn onto a floured surface; knead until smooth and elastic, 4-6 minutes, adding remaining flour if necessary to keep dough from sticking. Cover and let rest 30 minutes.
Meanwhile, in a large bowl, combine lobster, ricotta, parmesan, lemon zest, sage, salt, thyme and pepper until well combined. Set aside.
Divide pasta dough in half; on a lightly floured surface, roll 1 portion to 1/16-in. thickness (or use a pasta roller). Keep pasta covered until ready to use. Pipe filling by tablespoonfuls 1 in. apart over half of pasta sheet. Fold sheet over; press down to seal. Cut into squares with a pastry wheel. Repeat with remaining dough and filling.
In a Dutch oven, bring salted water to a boil; add ravioli. Reduce heat to a gentle simmer; cook until ravioli float to the top and are tender, 1-2 minutes.
Meanwhile, in a small saucepan, melt butter over medium heat. Add garlic; cook and stir 1 minute. Stir in wine. Cook and stir until reduced by half. Gradually stir in cream and sage. Bring to a gentle boil. Reduce heat; simmer, uncovered, until slightly thickened 3-5 minutes, stirring constantly. Reduce heat to low.
Gradually whisk in grated Parmesan. Return to a simmer. Cook and stir until just thick enough to coat a metal spoon. Stir in salt and pepper.
Drain ravioli; add to sauce and toss to coat.