The phrase "lay with" is a euphemism meaning that she had sexual relations with her father. Alternate translation: "I had sexual relations with my father ... have sexual relations with him" (See: [[rc://en/ta/man/jit/figs-euphemism]])
It can be made explicit that their goal was to get him drunk. Alternate translation: "drink wine until he gets drunk" or "get drunk with wine" (See: [[rc://en/ta/man/jit/figs-explicit]])
This speaks about giving Lot descendants as if his family were a line that they are making longer. Alternate translation: "so that we can bear children who will be our father's descendants" (See: [[rc://en/ta/man/jit/figs-metaphor]])