Combine 1/4 cup of the lemon juice and 1/4 cup water in a 2- to 2-1/2-quart non-aluminum Saucepan. One at a time, halve the pears lengthwise, remove the core, and peel; then slice the flesh thinly, dropping the slivers directly into the acidulated water to prevent discoloration.

Add 3/4 cup sugar and stir to combine. Bring the mixture to a gentle simmer over moderate heat, stirring to dissolve the sugar. Cover and simmer for 8 minutes. Remove the pot from the heat and let the mixture steep for 15 minutes. Once cooked, the pears can be refrigerated in their juices for 1 to 2 days.

Purée the pear mixture, either still hot or cold, in a food processor. Scrape the purée into a non-aluminum bowl and stir in the half-and-half. Add sugar if and as needed to bring out the flavor of the pears; the mixture should taste a bit too sweet at room temperature if it is to taste perfect when frozen. Add up to 2 tablespoons more lemon juice to round out the flavor. Stir in the pear liqueur.

Freeze the mixture in an ice cream maker according to manufacturer's instructions. Ripen the soft mixture in a freezer with a sheet of plastic wrap pressed directly on the surface. Let soften slightly before serving.