In the bowl of a stand mixer fitted with the paddle attachment, beat cream cheese and sugar at medium speed until smooth and creamy, 2 to 3 minutes, stopping to scrape sides of bowl. Add lemon juice, nutmeg, and vanilla, and beat just until combined, about 1 minute. With mixer on low speed, gradually add cold cream, beating until combined, 1 to 2 minutes; thoroughly scrape sides of bowl. Slowly increase mixer speed to medium-high, and beat until light and fluffy and stiff peaks form, 1 to 2 minutes. Pour into prepared pan, smoothing top with a small offset spatula. Freeze until firm, at least 2 hours.