Sprinkle gelatin over 1/2 cup lime juice in a small saucepan; let stand 1 minute. Add lime zest and 1/2 cup whipping cream. Cook over low heat, stirring until gelatin dissolves (about 2 minutes). Cool slightly.
Whisk together mascarpone cheese and 1 cup sugar. Slowly whisk in remaining 2 cups whipping cream. Gradually whisk in gelatin mixture. Pour into 8 dessert glasses; cover and chill 8 hours or overnight.
Combine remaining 1/2 cup sugar, remaining 1/4 cup lime juice, and butter in a small saucepan. Cook over low heat until sugar dissolves. Bring to a boil, reduce heat, and simmer 3 minutes. Cool completely. Pour mixture over strawberries, tossing to coat. Spoon strawberry mixture over chilled panna cotta.