In large stainless steel bowl, whisk condensed and evaporated milks. Add 1 cup (250 mL) lime juice. Whisk vigorously until thickened and slightly curdled looking, about 1 minute.
In 9-inch by 13-inch (22.5 cm by 32.5 cm) baking dish, pour 1-1/4 cups (310 mL) milk mixture over bottom, tilting pan to evenly cover and spreading with rubber spatula if needed. Gently place one layer of cookies side by side, barely touching, breaking some cookies in half to make them fit. (You should have about 12 whole cookies and five half cookies.) Pour another 1-1/2 cups (310 mL) milk mixture over cookies, spreading gently with spatula and making sure cookies are fully covered. Continue to add cookie layers and milk layers, alternating the spots where the whole and half cookies are, and finishing with milk layer. You should have four cookie layers and five milk layers.
Cover dish with plastic wrap without touching mixture. Refrigerate at least 3 hours to set.
To serve, cut as desired. Use microplane to zest 2 limes on top of each piece. Drizzle with lime juice and olive oil.
Refrigerate up to 2 days