Combine the strawberries and lemon juice in a medium saucepan and cook it over medium heat, stirring until the fruit has broken dow and is very soft, 8-10 minutes.
Transfer the fruit mixture to a mixing bowl and refrigerate it uncovered until it's completely cooled, about 30 minutes.
While the fruit is cooling, set the ice cream or sorbet out on the counter to soften for a few minutes (5-10) at room temperature. You want it to be soft and workable but not liquid.
Pour a tablespoon of fruit in the bottom of one of six, 3oz popsicle molds then add 2 tablespoons of softened ice cream or sorbet and alternate the fruit and ice cream in layers until they're full.
Insert the popsicle sticks and freeze them until they're solid, at least 6 hours, or up to 3 weeks.