I'm almost out of food. Then I waited for it to rain, but the villager went off right when it lifted. What now? Can I try again?

I suggest keeping an eye out for Rain. Then get an Adult Villager and put them on the Lift. You have to wait until it gets all the way up, then a Seed will fall. It should be next to the Lift.

The villagers will not stay on the lift indefinitely. If you put them on the lift before it rains, they may get bored and walk off just when you need them to stay there. It's better to keep a close eye on the game and place a villager on the lift as soon as it starts to rain.