Pack cucumbers, lemon rounds, and garlic into a 1 pint glass jar with lid.
In a small saucepan over medium heat, combine tomato juice, lemon juice, horseradish, peppercorns, salt, and hot sauce. Bring to boil, stirring occasionally. Remove from heat and stir in vodka.
Pour tomato juice mixture over cucumbers. Wipe the rim clean and seal with a lid. Allow to cool completely, then refrigerate until cold. The longer they sit, the better they taste. Store in the refrigerator for up to 3 weeks.