Whisk the honey, arrowroot, cream and salt together in a medium saucepan over medium heat. Bring the mixture to a simmer, while whisking constantly for 1-2 minutes until it thickens.
Remove from the heat and whisk in the sour cream a little bit at a time so it doesn’t curdle. Whisk in the lemon juice and pour mixture into a large bowl. Cover the bowl tightly and refrigerate for 3 hours, or until completely chilled. As an alternative, you can fill a large bowl with ice and set the bowl of lemon cream on top. The cream mixture should be cold enough to put into the ice cream maker in about 45 minutes.
Freeze the mixture in the ice cream maker according to the manufacturer’s instructions. Here is the ice cream maker I use. I purchased it over 20 years ago and it’s still working perfectly!