Halve the limes and cut 4 thin slices. Peel the peel thinly and squeeze the limes. Bring the juice with the sugar to the boil briefly and then simmer until the sugar has completely dissolved. Then let it cool down.
Mix the lime syrup with the cold mineral water, the vodka and the lemon ice cream properly. Decorate 4 glasses with the lime slices and the peel and pour in the shake.