Fill a large bowl with ice and a small amount of water.
Bring the cream and ginger to a boil in a saucepan.
Remove from heat and cover to infuse for 30 minutes.
Return the saucepan to the heat and bring it back to a boil.
Whisk the egg yolks and sugar together in a separate bowl.
Slowly whisk a portion of the hot cream into the egg yolk mixture.
Cook the combined mixture gently until it coats the back of a spoon.
Stir the butternut squash purée into the custard mixture.
Place the saucepan in the prepared ice bath to chill.
Stir in the lemon juice and pass the mixture through a fine sieve.
Churn the mixture in an ice cream machine and freeze until firm.