Pour the heavy whipping cream into a heavy-bottomed saucepan or double boiler.
Place over medium-low heat and slowly bring the temperature to exactly 185°F (85°C), monitoring constantly with a digital thermometer to prevent scorching.
Once at 185°F, reduce heat to low to maintain this temperature. Stir in the lemon juice gently.
Continue to cook at 185°F for 5 minutes, stirring occasionally. The mixture will thicken slightly and coat the back of a spoon (similar to crème anglaise).
Remove the pan from the heat and let it cool completely to room temperature naturally (about 30-45 minutes). Do not rush this step.
Line a fine-mesh sieve with 4 layers of cheesecloth or a clean coffee filter and place it over a bowl to catch the whey.
Pour the cooled cream mixture into the lined sieve.
Cover loosely with plastic wrap and refrigerate for 12 to 24 hours. The longer it drains, the thicker the mascarpone will be.
Transfer the thickened cheese to an airtight container. Use within 5 days.