Soak the red onion slices in cold water for half an hour, then drain. This will mellow their flavor.
Slice the focaccia horizontally so that you have a top and bottom. Spread the tapenade over the bottom piece, then cover with the lettuce, tomato, feta, cucumber, and red onion. Sprinkle with salt, pepper, and oregano. If you plan to eat the sandwich right away, drizzle the combined oil and vinegar over the onion, then top with the other piece of focaccia.
If you're not eating it right away, mix the vinegar and olive oil and put into a container. Wrap in foil or wax paper and transport the sandwich to your picnic whole, then take off the top slice of focaccia and drizzle the sandwich with the oil and vinegar.
Replace the top slice of bread, and cut the sandwich into 4 or 6 pieces.