In a half-gallon pitcher, combine water and Caramel Apple Cider Mix. Stir to dissolve. Let cool slightly.
Stir in vodka. Chill 2 hours or up to overnight.
Place lemon juice in a shallow dish. Slice apples crosswise into 12 thin, disc-like slices; gently remove seeds. Cut a slit into each slice. Dip into lemon juice and pat dry. Place on rim of 12 martini glasses.